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AGL(1,𝔽₅)×(C₃⋊D₃)⋊C₉ #72247368

order	3240
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

AGL(1,𝔽₅)×(C₃⋊D₃)⋊C₉

Splittings

Fitting, Hall	C₅×C₃²⋊C₉ ⋊ C₂×C₄
derived	C₃²×C₅ ⋊ C₂×C₄×C₉
Sylow	C₃²⋊C₉ ⋊ C₂×AGL(1,𝔽₅)
Sylow	C₅ ⋊ C₄×(C₃⋊D₃)⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃	AGL(1,𝔽₅)×(C₃⋊D₃)⋊C₃
commutator, hypocenter	C₃²×C₅	C₂×C₄×C₉
Frattini	C₃²	C₃×D₃×AGL(1,𝔽₅)
Fitting	C₅×C₃²⋊C₉	C₂×C₄
socle	C₃²×C₅	C₃×C₄×D₃
prime radical	C₃×D₅×C₃⋊D₃	C₂×C₃
cosocle	C₃³×D₅	C₂²×C₃
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₃

212 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 90

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₅)×((C₃⋊D₃)⋊C₉)⋊C₂, AGL(1,𝔽₅)×#92259
maximal normal subgroup of	AGL(1,𝔽₅)×((C₃⋊D₃)⋊C₉)⋊C₂, AGL(1,𝔽₅)×#92259

GAP

Past the SmallGroups library coverage — no SmallGroups id.