D₉×(C₂²⋊C₉)⋊C₂ #13048064

order	1296
isoclinism	isoclinic class of D₉×(C₂²⋊C₉)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂²

Aliases

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

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₉×C₂²⋊C₉	C₂²
Frattini	C₃²	D₃×S₄
Fitting	C₂²×C₃×C₉	C₂×D₃
socle	C₂²×C₃²	D₃²
LCS	G ▷ C₉×C₂²⋊C₉
UCS	C₁

202 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.

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

μ_t(G) = 72

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 1782);