D₅₅×C₃₁⋊C₉ #44501710

order	30690
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₅₅×C₃₁⋊C₉
unambiguous semidirect product	C₅⋊(D₁₁×C₃₁⋊C₉)
unambiguous semidirect product	C₁₁⋊(D₅×C₃₁⋊C₉)
unambiguous semidirect product	(C₃₁×D₅₅)⋊C₉

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₃₁⋊C₃×D₅₅
commutator, hypocenter	C₅×C₁₁×C₃₁	C₂×C₉
Fitting, socle, cosocle	C₃×C₅×C₁₁×C₃₁	C₂×C₃
prime radical	C₃×C₃₁×D₅₅	C₃
LCS	G ▷ C₅×C₁₁×C₃₁
UCS	C₁ ◁ C₃

48 conjugacy classes of subgroups.

μ_t(G) = 15345

1131 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 77);