C₃₁×H(3,𝔽₇) #24922344

order	10633
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₇²×C₃₁ · Schur multiplier (H₂) = C₇²

Aliases

direct product	C₃₁×H(3,𝔽₇)
unambiguous semidirect product	C₇²⋊(C₇×C₃₁)
unambiguous semidirect product	(C₇²×C₃₁)⋊C₇

	subgroup	G/H
center, socle	C₇×C₃₁	C₇²
commutator, Frattini, cosocle	C₇	C₇²×C₃₁
LCS	G ▷ C₇ ▷ C₁
UCS	C₁ ◁ C₇×C₃₁ ◁ G

38 conjugacy classes of subgroups.

1705 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10633, 3);