C₇×C₁₁₇₁⋊C₃ #37589678

order	24591
automorphism	?
homology	Abelianization (H₁) = C₃×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₁₇₁⋊C₃
unambiguous semidirect product	C₁₁₇₁⋊(C₃×C₇)

Fitting, socle, Hall	C₇×C₁₁₇₁ ⋊ C₃
derived, Sylow	C₁₁₇₁ ⋊ C₃×C₇

	subgroup	G/H
center, hypercenter	C₇	C₁₁₇₁⋊C₃
commutator, cosocle, hypocenter	C₁₁₇₁	C₃×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₁₇₁	C₃
LCS	G ▷ C₁₁₇₁
UCS	C₁ ◁ C₇

8 conjugacy classes of subgroups.

μ_t(G) = 8197

2751 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24591, 2);