C₃×A₄×C₆₈₃ #37589666

order	24588
automorphism	?
homology	Abelianization (H₁) = C₃²×C₆₈₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×A₄×C₆₈₃
unambiguous semidirect product	C₂²⋊(C₃²×C₆₈₃)
unambiguous semidirect product	(C₂²×C₃)⋊(C₃×C₆₈₃)
unambiguous semidirect product	(C₂²×C₆₈₃)⋊C₃²
unambiguous semidirect product	(C₂²×C₃×C₆₈₃)⋊C₃

	subgroup	G/H
center, hypercenter	C₃×C₆₈₃	A₄
commutator, cosocle, hypocenter	C₂²	C₃²×C₆₈₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₆₈₃	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₆₈₃

28 conjugacy classes of subgroups.

μ_t(G) = 8196

8196 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24588, 25);