C₂×C₅×C₃₁×C₇⋊D₇ #44477198

order	30380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₃₁ · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	C₂×C₅×C₃₁×C₇⋊D₇
unambiguous semidirect product	(C₂×C₇)⋊(C₅×D₇×C₃₁)

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

200 conjugacy classes of subgroups.

μ_t(G) = 15190

8060 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30380, 107);