C₇×#2546 #11741855

order	896
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁵

Aliases

	subgroup	G/H
center, socle, prime radical	C₂³×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

540 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 896

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(896, 16621);