C₂×D₁₁₇ #90842

order	468
isoclinism	isoclinic class of D₁₁₇
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₂₃₄
direct product	C₂×D₁₁₇
unambiguous semidirect product	(C₂×C₉)⋊D₁₃
unambiguous semidirect product	(C₂×C₁₃)⋊D₉

	subgroup	G/H
center, hypercenter	C₂	D₁₁₇
commutator, cosocle, hypocenter	C₉×C₁₃	C₂²
Frattini	C₃	C₂×D₃₉
Fitting	C₂×C₉×C₁₃	C₂
socle	C₂×C₃×C₁₃	D₃
LCS	G ▷ C₉×C₁₃
UCS	C₁ ◁ C₂

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 234

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2)(3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24);(4,11)(5,10)(6,9)(7,8)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 17);