C₂⁴×(C₂²⋊C₉)⋊C₂ #11923437

order	1152
isoclinism	isoclinic class of (C₂²⋊C₉)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹¹

Aliases

direct product	C₂⁴×(C₂²⋊C₉)⋊C₂
unambiguous semidirect product	(C₂²⋊C₉)⋊C₂⁵
unambiguous semidirect product	(C₂×C₂²⋊C₉)⋊C₂⁴

C₂²⋊C₉ ⋊ C₂⁵

	subgroup	G/H
center, hypercenter	C₂⁴	(C₂²⋊C₉)⋊C₂
commutator, cosocle, hypocenter	C₂²⋊C₉	C₂⁵
Frattini	C₃	C₂⁴×S₄
Fitting, socle	C₂⁶×C₃	D₃
LCS	G ▷ C₂²⋊C₉
UCS	C₁ ◁ C₂⁴

9506 conjugacy classes of subgroups; only the 642 normal subgroups are shown.

normal subgroups only

This group has 9506 conjugacy classes of subgroups — too many to draw. Only its 642 normal subgroups are shown.

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

μ_t(G) = 144

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 157448);