C₅×C₁₃×D₂₄₉ #44569160

order	32370
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₃×D₂₄₉
unambiguous semidirect product	C₃⋊(C₅×C₁₃×D₈₃)
unambiguous semidirect product	C₈₃⋊(C₅×D₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₅×C₁₃	D₂₄₉
commutator, cosocle, hypocenter	C₃×C₈₃	C₂×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₈₃	C₂
LCS	G ▷ C₃×C₈₃
UCS	C₁ ◁ C₅×C₁₃

32 conjugacy classes of subgroups.

μ_t(G) = 16185

8190 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32370, 11);