C₃×A₄×C₁₇² #23780940

order	10404
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₇² · Schur multiplier (H₂) = C₂×C₃×C₁₇

Aliases

direct product	C₃×A₄×C₁₇²
unambiguous semidirect product	C₂²⋊(C₃²×C₁₇²)
unambiguous semidirect product	(C₂²×C₃)⋊(C₃×C₁₇²)
unambiguous semidirect product	(C₂²×C₁₇)⋊(C₃²×C₁₇)
unambiguous semidirect product	(C₂²×C₃×C₁₇)⋊(C₃×C₁₇)

	subgroup	G/H
center, hypercenter	C₃×C₁₇²	A₄
commutator, cosocle, hypocenter	C₂²	C₃²×C₁₇²
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₇²	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₁₇²

280 conjugacy classes of subgroups.

3468 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10404, 150);