C₃²×((C₂²⋊C₉)⋊C₂)⋊C₃ #14519191

order	1944
isoclinism	isoclinic class of ((C₂²⋊C₉)⋊C₂)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃³ · Schur multiplier (H₂) = C₂×C₃³

Aliases

direct product	C₃²×((C₂²⋊C₉)⋊C₂)⋊C₃
unambiguous semidirect product	((C₂²⋊C₉)⋊C₂)⋊C₃³
unambiguous semidirect product	(C₃×(C₂²⋊C₉)⋊C₂)⋊C₃²

	subgroup	G/H
center, hypercenter	C₃²	((C₂²⋊C₉)⋊C₂)⋊C₃
commutator, cosocle, hypocenter	C₂²⋊C₉	C₂×C₃³
Frattini	C₃	C₃³×S₄
Fitting	C₂²×C₃⁴	D₃
socle	C₂²×C₃³	C₃×D₃
LCS	G ▷ C₂²⋊C₉
UCS	C₁ ◁ C₃²

786 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 124 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(1944, 3585);