C₃×D₃×(C₂²⋊C₉)⋊C₂ #13049203

order	1296
isoclinism	isoclinic class of D₃×(C₂²⋊C₉)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²

Aliases

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

298 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.

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

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 72

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2921);