Dihedral Group D_5
The group 👁 D_5
is one of the two groups of order 10. Unlike the cyclic
group 👁 C_(10)
,
👁 D_5
is non-Abelian. The molecule ruthenocene
👁 (C_5H_5)_2Ru
belongs to the group 👁 D_(5h)
, where the letter 👁 h
indicates invariance under a reflection of the fivefold axis
(Arfken 1985, p. 248).
👁 D_5
has cycle
index given by
Its multiplication table is illustrated above.
The dihedral group 👁 D_5
has conjugacy classes 👁 {1}
,
👁 {B,C}
, 👁 {A,D}
, and 👁 {E,F,G,H,I}
. It has 8 subgroups: 👁 {1}
, 👁 {1,E}
, 👁 {1,F}
, 👁 {1,G}
, 👁 {1,H}
, 👁 {1,I}
, 👁 {1,A,B,C,D}
, and 👁 {1,A,B,C,D,E,F,G,H,I}
, of which 👁 {1}
, 👁 {1,A,B,C,D}
, and 👁 {1
, 👁 A
, 👁 B
, 👁 C
, 👁 D
, 👁 E
, 👁 F
, 👁 G
, 👁 H
, 👁 I}
are normal.
See also
Dihedral Group, Dihedral Group D3, Dihedral Group D4Explore with Wolfram|Alpha
More things to try:
References
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, p. 248, 1985.Referenced on Wolfram|Alpha
Dihedral Group D_5Cite this as:
Weisstein, Eric W. "Dihedral Group D_5." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DihedralGroupD5.html