C₃₇×AΣL(1,𝔽₂₇) #15688491

order	2997
nilpotency class	3
isoclinism	isoclinic class of AΣL(1,𝔽₂₇)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₃₇ · Schur multiplier (H₂) = C₃

Aliases

	subgroup	G/H
center, socle	C₃×C₃₇	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₃²×C₃₇
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₃₇ ◁ C₃²×C₃₇ ◁ G

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 333

A minimal faithful permutation representation — 2 generators on 46 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(38,39,41)(40,42,45)(43,46,44);(39,42,43)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2997, 7);