C₂³×C₃×(C₂²⋊C₉)⋊C₂ #13180079

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

Aliases

C₂²⋊C₉ ⋊ C₂⁴×C₃

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

2714 conjugacy classes of subgroups; only the 262 normal subgroups are shown.

normal subgroups only

This group has 2714 conjugacy classes of subgroups — too many to draw. Only its 262 normal subgroups are shown.

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

μ_t(G) = 144

maximal subgroup of	C₂×C₂²⋊C₉×(C₂²⋊C₉)⋊C₂, C₂³×C₃×((C₂²⋊C₉)⋊C₂)⋊C₃, C₂×#72220166
maximal normal subgroup of	C₂×C₂²⋊C₉×(C₂²⋊C₉)⋊C₂, C₂³×C₃×((C₂²⋊C₉)⋊C₂)⋊C₃, C₂×#72220166

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 46142);