C₂×C₃⋊(((C₂²⋊C₉)⋊C₂)⋊C₃) #13049283

order	1296
isoclinism	isoclinic class of C₃⋊(((C₂²⋊C₉)⋊C₂)⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²×C₃

Aliases

direct product	C₂×C₃⋊(((C₂²⋊C₉)⋊C₂)⋊C₃)
unambiguous semidirect product	(C₂×C₃)⋊(((C₂²⋊C₉)⋊C₂)⋊C₃)

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(((C₂²⋊C₉)⋊C₂)⋊C₃)
commutator, cosocle, hypocenter	C₃×C₂²⋊C₉	C₂²×C₃
Frattini	C₃	C₂×C₃×C₃⋊S₄
Fitting	C₂³×C₃³	D₃
socle	C₂³×C₃²	C₃×D₃
LCS	G ▷ C₃×C₂²⋊C₉
UCS	C₁ ◁ C₂

424 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

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

μ_t(G) = 54

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 3001);