C₂×C₉⋊((C₂²⋊C₉)⋊C₂) #13048115

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

Aliases

direct product	C₂×C₉⋊((C₂²⋊C₉)⋊C₂)
unambiguous semidirect product	(C₂×C₉)⋊((C₂²⋊C₉)⋊C₂)
unambiguous semidirect product	(C₂×C₂²⋊C₉)⋊D₉

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

360 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.

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

μ_t(G) = 162

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 1833);