C₂×C₇×D₇×ΓL(1,𝔽₃₂) #44477156

order	30380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₇×D₇×ΓL(1,𝔽₃₂)
unambiguous semidirect product	C₇⋊(C₂²×C₇×ΓL(1,𝔽₃₂))
unambiguous semidirect product	(C₂×C₇)⋊(C₂×C₇×ΓL(1,𝔽₃₂))
unambiguous semidirect product	(C₂×D₇×C₃₁)⋊(C₅×C₇)
unambiguous semidirect product	(C₂×C₇×D₇×C₃₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₂×C₇	D₇×ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₇×C₃₁	C₂²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₃₁	C₂×C₅
LCS	G ▷ C₇×C₃₁
UCS	C₁ ◁ C₂×C₇

104 conjugacy classes of subgroups.

μ_t(G) = 868

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30380, 65);