C₃²×C₁₁×H(3,𝔽₃) #14582014

order	2673
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃⁴×C₁₁ · Schur multiplier (H₂) = C₃⁷

Aliases

direct product	C₃²×C₁₁×H(3,𝔽₃)
unambiguous semidirect product	C₃²⋊(C₃³×C₁₁)
unambiguous semidirect product	(C₃²×C₁₁)⋊C₃³

	subgroup	G/H
center, socle	C₃³×C₁₁	C₃²
commutator, Frattini, cosocle	C₃	C₃⁴×C₁₁
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃³×C₁₁ ◁ G

900 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 891

A minimal faithful permutation representation — 4 generators on 26 points:

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

1089 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2673, 62);