C₅×C₁₀₅₁⋊C₇ #49145454

order	36785
automorphism	?
homology	Abelianization (H₁) = C₅×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₀₅₁⋊C₇
unambiguous semidirect product	(C₅×C₁₀₅₁)⋊C₇

Fitting, socle, Hall	C₅×C₁₀₅₁ ⋊ C₇
derived, Sylow	C₁₀₅₁ ⋊ C₅×C₇

	subgroup	G/H
center, hypercenter	C₅	C₁₀₅₁⋊C₇
commutator, cosocle, hypocenter	C₁₀₅₁	C₅×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₀₅₁	C₇
LCS	G ▷ C₁₀₅₁
UCS	C₁ ◁ C₅

8 conjugacy classes of subgroups.

μ_t(G) = 5255

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36785, 2);