C₅×C₄₇×C₇⋊D₇ #37527837

order	23030
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₄₇ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₅×C₄₇×C₇⋊D₇
unambiguous semidirect product	C₇⋊(C₅×D₇×C₄₇)

	subgroup	G/H
center, hypercenter	C₅×C₄₇	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₅×C₄₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₄₇	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₅×C₄₇

80 conjugacy classes of subgroups.

μ_t(G) = 11515

6110 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23030, 13);