C₂³×((C₂²⋊C₉)⋊C₂)⋊C₃ #13180080

order	1728
isoclinism	isoclinic class of ((C₂²⋊C₉)⋊C₂)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product	C₂³×((C₂²⋊C₉)⋊C₂)⋊C₃
unambiguous semidirect product	((C₂²⋊C₉)⋊C₂)⋊(C₂³×C₃)
unambiguous semidirect product	#1094⋊C₂⁴
unambiguous semidirect product	(C₂×#1094)⋊C₂³

C₂²⋊C₉ ⋊ C₂⁴×C₃

	subgroup	G/H
center, hypercenter	C₂³	((C₂²⋊C₉)⋊C₂)⋊C₃
commutator, cosocle, hypocenter	C₂²⋊C₉	C₂⁴×C₃
Frattini	C₃	C₂³×C₃×S₄
Fitting	C₂⁵×C₃²	D₃
socle	C₂⁵×C₃	C₃×D₃
LCS	G ▷ C₂²⋊C₉
UCS	C₁ ◁ C₂³

2682 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 2682 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.

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

μ_t(G) = 72

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 46143);