C₇⋊#595 #90914

order	476
isoclinism	isoclinic class of C₇⋊#595
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇×C₁₇	C₄
prime radical, cosocle	C₇×D₁₇	C₂
LCS	G ▷ C₇×C₁₇
UCS	C₁

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 119

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

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

Polycyclic presentation:

2^2,7,17|a^2=b,c^a=c^6,d^a=d^4,d^b=d^16

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(476, 6);