C₃×D₅×C₁₁×C₈₉ #44440322

order	29370
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₁×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₅×C₁₁×C₈₉
unambiguous semidirect product	C₅⋊(C₂×C₃×C₁₁×C₈₉)

	subgroup	G/H
center, hypercenter	C₃×C₁₁×C₈₉	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃×C₁₁×C₈₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₈₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₁₁×C₈₉

32 conjugacy classes of subgroups.

μ_t(G) = 14685

11748 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29370, 7);