C₁₅₇×C₆₇⋊C₃ #44538819

order	31557
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₅₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₅₇×C₆₇⋊C₃
unambiguous semidirect product	C₆₇⋊(C₃×C₁₅₇)

Fitting, socle, Hall	C₆₇×C₁₅₇ ⋊ C₃
derived, Sylow	C₆₇ ⋊ C₃×C₁₅₇

	subgroup	G/H
center, hypercenter	C₁₅₇	C₆₇⋊C₃
commutator, cosocle, hypocenter	C₆₇	C₃×C₁₅₇
Frattini	C₁	G
Fitting, socle	C₆₇×C₁₅₇	C₃
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₁₅₇

8 conjugacy classes of subgroups.

μ_t(G) = 10519

3925 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31557, 1);