C₂²×#63690 #11921400

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center	C₂³	C₂×(C₂²⋊C₉)⋊C₂
commutator, cosocle, hypocenter	Q₈⋊C₉	C₂⁴
Frattini	C₂×C₃	C₂³×S₄
Fitting, prime radical	C₂²×C₃×#41	D₃
socle	C₂³×C₃	C₂×S₄
hypercenter	C₂²×C₄	(C₂²⋊C₉)⋊C₂
LCS	G ▷ Q₈⋊C₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

1341 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 1341 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.

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

μ_t(G) = 576

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 155411);