C₂×D₇×C₃₁×C₃₇ #44545809

order	32116
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃₁×C₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₇×C₃₁×C₃₇
unambiguous semidirect product	C₇⋊(C₂²×C₃₁×C₃₇)
unambiguous semidirect product	(C₂×C₇)⋊(C₂×C₃₁×C₃₇)

	subgroup	G/H
center, hypercenter	C₂×C₃₁×C₃₇	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₃₁×C₃₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₃₁×C₃₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃₁×C₃₇

40 conjugacy classes of subgroups.

μ_t(G) = 16058

11470 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32116, 24);