C₂×C₃²×(C₂²⋊C₉)⋊C₂ #13049271

order	1296
isoclinism	isoclinic class of (C₂²⋊C₉)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂²×C₃

Aliases

	subgroup	G/H
center, hypercenter	C₂×C₃²	(C₂²⋊C₉)⋊C₂
commutator, cosocle, hypocenter	C₂²⋊C₉	C₂²×C₃²
Frattini	C₃	C₂×C₃²×S₄
Fitting, socle	C₂³×C₃³	D₃
LCS	G ▷ C₂²⋊C₉
UCS	C₁ ◁ C₂×C₃²

432 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 78 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, 2989);