C₂×C₇×D₁₇ #90916

order	476
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₇×D₁₇
unambiguous semidirect product	C₁₇⋊(C₂²×C₇)
unambiguous semidirect product	(C₂×C₁₇)⋊(C₂×C₇)

	subgroup	G/H
center, hypercenter	C₂×C₇	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₇

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 238

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2)(3,4,5,6,7,8,9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);(1,2)(10,11,13,15,17,19,21,23,25,26,24,22,20,18,16,14,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(476, 8);