C₂×C₃²×D₃×A₄ #13049872

order	1296
isoclinism	isoclinic class of D₃×A₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃³ · Schur multiplier (H₂) = C₂²×C₃³

Aliases

direct product	C₂×C₃²×D₃×A₄
unambiguous semidirect product	C₃⋊(C₂²×C₃²×A₄)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₃²×A₄)
unambiguous semidirect product	(C₂³×D₃)⋊C₃³
unambiguous semidirect product	(C₂³×C₃×D₃)⋊C₃²

Fitting, socle	C₂³×C₃³ ⋊ C₂×C₃
derived	C₂²×C₃ ⋊ C₂²×C₃³

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₃×A₄
commutator, cosocle, hypocenter	C₂²×C₃	C₂²×C₃³
Frattini	C₁	G
Fitting, socle	C₂³×C₃³	C₂×C₃
LCS	G ▷ C₂²×C₃
UCS	C₁ ◁ C₂×C₃²

1132 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 1132 conjugacy classes of subgroups — too many to draw. Only its 238 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 108

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 3590);