C₇×#3171 #11742480

order	896
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center	C₂×C₄×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄²×C₇ ◁ G

408 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 448

A minimal faithful permutation representation — 4 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(896, 17246);