C₂²×C₇×#533 #13239883

order	1792
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₇ · Schur multiplier (H₂) = C₂¹³

Aliases

C₂²×C₇×#533

	subgroup	G/H
center	C₂³×C₄×C₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
socle	C₂⁴×C₇	C₂⁴
prime radical	C₂⁵×C₇	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₇ ◁ G

8238 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 896

A minimal faithful permutation representation — 6 generators on 27 points:

(1,2)(21,22,23,24,25,26,27);(3,4);(5,6)(7,10)(8,9)(11,12)(13,14,16,18)(15,19,20,17);(6,9)(10,12);(13,15,16,20)(14,17,18,19);(5,7,8,11)(6,10,9,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 55655);