C₇×#19747 #13196963

order	1792
nilpotency class	3
isoclinism	isoclinic class of #19745
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄²×C₇ ◁ G

908 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)(9,12)(10,13)(14,15)(17,20)(18,22)(21,23);(8,9,13,15,11,14,10,12);(16,17,18,20,19,21,22,23);(9,14)(12,15)(17,21)(20,23)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 12735);