C₃×((C₂²⋊C₂₇)⋊C₂)⋊C₃ #14517963

order	1944
isoclinism	isoclinic class of ((C₂²⋊C₂₇)⋊C₂)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×((C₂²⋊C₂₇)⋊C₂)⋊C₃
unambiguous semidirect product	((C₂²⋊C₂₇)⋊C₂)⋊C₃²
unambiguous semidirect product	(C₃×(C₂²⋊C₂₇)⋊C₂)⋊C₃

C₂²⋊C₂₇ ⋊ C₂×C₃²

	subgroup	G/H
center, hypercenter	C₃	((C₂²⋊C₂₇)⋊C₂)⋊C₃
commutator, cosocle, hypocenter	C₂²⋊C₂₇	C₂×C₃²
Frattini	C₉	C₃²×S₄
Fitting	C₂²×C₃²×C₉	D₃
socle	C₂²×C₃²	C₃×D₉
LCS	G ▷ C₂²⋊C₂₇
UCS	C₁ ◁ C₃

202 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

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

μ_t(G) = 108

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2357);