C₂²×C₃×(C₂²⋊C₉)⋊C₂ #11724044

order	864
isoclinism	isoclinic class of (C₂²⋊C₉)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂⁴

Aliases

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

499 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 499 conjugacy classes of subgroups — too many to draw. Only its 72 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(864, 4011);