C₃²×C₈₃⋊C₄₁ #44499537

order	30627
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄₁ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×C₈₃⋊C₄₁
unambiguous semidirect product	C₈₃⋊(C₃²×C₄₁)
unambiguous semidirect product	(C₃×C₈₃)⋊(C₃×C₄₁)
unambiguous semidirect product	(C₃²×C₈₃)⋊C₄₁

Fitting, socle, Hall	C₃²×C₈₃ ⋊ C₄₁
derived, Sylow	C₈₃ ⋊ C₃²×C₄₁

	subgroup	G/H
center, hypercenter	C₃²	C₈₃⋊C₄₁
commutator, cosocle, hypocenter	C₈₃	C₃²×C₄₁
Frattini	C₁	G
Fitting, socle	C₃²×C₈₃	C₄₁
LCS	G ▷ C₈₃
UCS	C₁ ◁ C₃²

24 conjugacy classes of subgroups.

μ_t(G) = 747

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30627, 4);