C₃×C₃⋊(C₃⋊((C₂²⋊C₉)⋊C₂)) #14519223

order	1944
isoclinism	isoclinic class of C₃⋊(C₃⋊((C₂²⋊C₉)⋊C₂))
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂×C₃³

Aliases

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

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₃⋊((C₂²⋊C₉)⋊C₂))
commutator, cosocle, hypocenter	C₃²×C₂²⋊C₉	C₂×C₃
Frattini	C₃	C₃×C₃⋊(C₃⋊S₄)
Fitting, socle	C₂²×C₃⁴	D₃
LCS	G ▷ C₃²×C₂²⋊C₉
UCS	C₁ ◁ C₃

942 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.

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

μ_t(G) = 324

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3617);