C₂²×C₁₃×C₁₂₁⋊C₅ #44538080

order	31460
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂²×C₁₃×C₁₂₁⋊C₅
unambiguous semidirect product	(C₂²×C₁₂₁)⋊(C₅×C₁₃)
unambiguous semidirect product	(C₂²×C₁₃×C₁₂₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₂²×C₁₃	C₁₂₁⋊C₅
commutator, cosocle, hypocenter	C₁₂₁	C₂²×C₅×C₁₃
Frattini	C₁₁	C₂²×C₁₃×C₁₁⋊C₅
Fitting	C₂²×C₁₃×C₁₂₁	C₅
socle	C₂²×C₁₁×C₁₃	C₁₁⋊C₅
LCS	G ▷ C₁₂₁
UCS	C₁ ◁ C₂²×C₁₃

60 conjugacy classes of subgroups.

μ_t(G) = 6292

1508 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 20);