C₃×A₄×C₂₃² #34039978

order	19044
automorphism	?
homology	Abelianization (H₁) = C₃²×C₂₃² · Schur multiplier (H₂) = C₂×C₃×C₂₃

Aliases

direct product	C₃×A₄×C₂₃²
unambiguous semidirect product	C₂²⋊(C₃²×C₂₃²)
unambiguous semidirect product	(C₂²×C₃)⋊(C₃×C₂₃²)
unambiguous semidirect product	(C₂²×C₂₃)⋊(C₃²×C₂₃)
unambiguous semidirect product	(C₂²×C₃×C₂₃)⋊(C₃×C₂₃)

	subgroup	G/H
center, hypercenter	C₃×C₂₃²	A₄
commutator, cosocle, hypocenter	C₂²	C₃²×C₂₃²
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₂₃²	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₂₃²

364 conjugacy classes of subgroups.

μ_t(G) = 6348

6348 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19044, 116);