Finite Group Databasebeta

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D₃×C₃⋊(D₉⋊C₉) #72243576

order	2916
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

D₃×C₃⋊(D₉⋊C₉)

Splittings

Fitting, Sylow	C₃²×C₉⋊C₉ ⋊ C₂²
derived	C₃²×C₉ ⋊ C₂²×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₃×C₃⋊AGL(1,ℤ/9)
commutator, hypocenter	C₃²×C₉	C₂²×C₉
Frattini	C₃²	C₃×D₃×C₃⋊D₃
Fitting	C₃²×C₉⋊C₉	C₂²
socle	C₃⁴	C₂×C₃×D₃
prime radical	C₃×D₃×C₃⋊D₉	C₃
cosocle	C₃³×C₉	C₂²×C₃
LCS	G ▷ C₃²×C₉
UCS	C₁ ◁ C₃

658 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 108

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃²×D₉⋊C₉, D₃×C₃⋊AGL(1,ℤ/27), D₃×C₃⋊#92265
maximal normal subgroup of	D₃²×D₉⋊C₉, D₃×C₃⋊#92265
maximal quotient of	D₃×C₃⋊AGL(1,ℤ/27)

GAP

Past the SmallGroups library coverage — no SmallGroups id.