C₅×D₃×C₂₃×C₅₃ #49143263

order	36570
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₂₃×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₃×C₂₃×C₅₃
unambiguous semidirect product	C₃⋊(C₂×C₅×C₂₃×C₅₃)

	subgroup	G/H
center, hypercenter	C₅×C₂₃×C₅₃	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₅×C₂₃×C₅₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₂₃×C₅₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₅×C₂₃×C₅₃

32 conjugacy classes of subgroups.

μ_t(G) = 18285

18285 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36570, 9);