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D₉×#87830 #72247443

order	7200
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

Splittings

derived, Hall	C₅²×C₉ ⋊ C₂×C₄²
Sylow	C₅² ⋊ C₄²×D₉
Sylow	C₉ ⋊ C₂×#87830

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉×D₅⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅²×C₉	C₂×C₄²
Frattini	C₂×C₃	D₃×D₅⋊AGL(1,𝔽₅)
Fitting	C₂×C₅²×C₉	C₂²×C₄
socle	C₂×C₃×C₅²	C₂×C₄×D₃
prime radical	C₂×D₉×C₅⋊D₅	C₂²
cosocle	C₂×C₉×C₅⋊D₅	C₂³
LCS	G ▷ C₅²×C₉
UCS	C₁ ◁ C₂

810 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 121 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) = 180

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₉×#11717375, AGL(1,ℤ/9)×#87830
maximal normal subgroup of	D₉×#11717375, AGL(1,ℤ/9)×#87830

GAP

Past the SmallGroups library coverage — no SmallGroups id.