C₃²×C₁₁₅₃⋊C₃ #44528086

order	31131
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃³

Aliases

direct product	C₃²×C₁₁₅₃⋊C₃
unambiguous semidirect product	C₁₁₅₃⋊C₃³
unambiguous semidirect product	(C₃×C₁₁₅₃)⋊C₃²

Fitting, socle	C₃²×C₁₁₅₃ ⋊ C₃
derived, Sylow	C₁₁₅₃ ⋊ C₃³

	subgroup	G/H
center, hypercenter	C₃²	C₁₁₅₃⋊C₃
commutator, cosocle, hypocenter	C₁₁₅₃	C₃³
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁₅₃	C₃
LCS	G ▷ C₁₁₅₃
UCS	C₁ ◁ C₃²

56 conjugacy classes of subgroups.

μ_t(G) = 10377

3483 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31131, 13);