H(3,𝔽₃)×C₃₁ #11719692

order	837
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₃₁ · Schur multiplier (H₂) = C₃²

Aliases

direct product	H(3,𝔽₃)×C₃₁
unambiguous semidirect product	C₃²⋊(C₃×C₃₁)

	subgroup	G/H
center, socle	C₃×C₃₁	C₃²
commutator, Frattini, cosocle	C₃	C₃²×C₃₁
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₃₁ ◁ G

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 279

A minimal faithful permutation representation — 2 generators on 40 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(837, 10);