C₆₇×C₁₅₇⋊C₃ #44538820

order	31557
automorphism	?
homology	Abelianization (H₁) = C₃×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

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

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

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

8 conjugacy classes of subgroups.

μ_t(G) = 10519

3685 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31557, 2);