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C₂×D₉×B(4,𝔽₂) #72252707

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹¹

Aliases

C₂×D₉×B(4,𝔽₂)

Splittings

Fitting	C₂×C₉×B(4,𝔽₂) ⋊ C₂
Sylow	C₉ ⋊ C₂²×B(4,𝔽₂)

Subgroups

	subgroup	G/H
center	C₂²	D₉×#120
commutator, cosocle	C₂³×C₉	C₂⁵
Frattini	C₂³×C₃	C₂⁴×D₃
Fitting	C₂×C₉×B(4,𝔽₂)	C₂
socle	C₂²×C₃	D₃×#120
hypercenter	C₂×B(4,𝔽₂)	D₉
hypocenter	C₉	C₂²×B(4,𝔽₂)
LCS	G ▷ C₂³×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂×B(4,𝔽₂)

10521 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	D₉×#23900, C₂×AGL(1,ℤ/9)×B(4,𝔽₂)
maximal normal subgroup of	D₉×#23900, C₂×AGL(1,ℤ/9)×B(4,𝔽₂)
maximal quotient of	D₉×#23900

GAP

Past the SmallGroups library coverage — no SmallGroups id.