C₁₃⋊C₃×C₈₂₉ #44568262

order	32331
automorphism	?
homology	Abelianization (H₁) = C₃×C₈₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃⋊C₃×C₈₂₉
unambiguous semidirect product	C₁₃⋊(C₃×C₈₂₉)

Fitting, socle, Hall	C₁₃×C₈₂₉ ⋊ C₃
derived, Sylow	C₁₃ ⋊ C₃×C₈₂₉

	subgroup	G/H
center, hypercenter	C₈₂₉	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₈₂₉
Frattini	C₁	G
Fitting, socle	C₁₃×C₈₂₉	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₈₂₉

8 conjugacy classes of subgroups.

μ_t(G) = 10777

5803 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32331, 1);