C₂²×((C₃⋊D₃)⋊C₉)⋊C₂ #13048140

order	1296
isoclinism	isoclinic class of ((C₃⋊D₃)⋊C₉)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product	C₂²×((C₃⋊D₃)⋊C₉)⋊C₂
unambiguous semidirect product	((C₃⋊D₃)⋊C₉)⋊C₂³
unambiguous semidirect product	#4169⋊C₂³
unambiguous semidirect product	#4181⋊C₂³

Fitting	C₂²×C₃²⋊C₉ ⋊ C₂²
derived, Sylow	C₃²⋊C₉ ⋊ C₂⁴

	subgroup	G/H
center, hypercenter	C₂²	((C₃⋊D₃)⋊C₉)⋊C₂
commutator, cosocle, hypocenter	C₃²⋊C₉	C₂⁴
Frattini	C₃²	C₂²×D₃²
Fitting	C₂²×C₃²⋊C₉	C₂²
socle	C₂²×C₃²	D₃²
LCS	G ▷ C₃²⋊C₉
UCS	C₁ ◁ C₂²

833 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 833 conjugacy classes of subgroups — too many to draw. Only its 135 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(1296, 1858);