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C₂×D₉×#453 #72244433

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂×D₉×#453

Splittings

Fitting	C₂×C₉×#453 ⋊ C₂
Sylow	C₉ ⋊ C₂²×#453

Subgroups

	subgroup	G/H
center	C₂²	D₉×#120
commutator, cosocle	C₂×C₄×C₉	C₂⁵
Frattini	C₂×C₃×C₄	C₂⁴×D₃
Fitting	C₂×C₉×#453	C₂
socle	C₂²×C₃	D₃×#120
hypercenter	C₂×#453	D₉
hypocenter	C₉	C₂²×#453
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#453

8505 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 144

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×AGL(1,ℤ/9)×#453, D₉×#61110
maximal normal subgroup of	C₂×AGL(1,ℤ/9)×#453, D₉×#61110

GAP

Past the SmallGroups library coverage — no SmallGroups id.