C₇²×C₁₃₁⋊C₅ #44545592

order	32095
automorphism	?
homology	Abelianization (H₁) = C₅×C₇² · Schur multiplier (H₂) = C₇

Aliases

direct product	C₇²×C₁₃₁⋊C₅
unambiguous semidirect product	C₁₃₁⋊(C₅×C₇²)
unambiguous semidirect product	(C₇×C₁₃₁)⋊(C₅×C₇)
unambiguous semidirect product	(C₇²×C₁₃₁)⋊C₅

Fitting, socle, Hall	C₇²×C₁₃₁ ⋊ C₅
derived, Sylow	C₁₃₁ ⋊ C₅×C₇²

	subgroup	G/H
center, hypercenter	C₇²	C₁₃₁⋊C₅
commutator, cosocle, hypocenter	C₁₃₁	C₅×C₇²
Frattini	C₁	G
Fitting, socle	C₇²×C₁₃₁	C₅
LCS	G ▷ C₁₃₁
UCS	C₁ ◁ C₇²

40 conjugacy classes of subgroups.

μ_t(G) = 6419

1519 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32095, 4);