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D₄²×D₉ #11902307

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

D₄²×D₉

Splittings

Fitting	D₄²×C₉ ⋊ C₂
Sylow	C₉ ⋊ C₂×D₄²

Subgroups

	subgroup	G/H
center	C₂²	C₂⁴×D₉
commutator, cosocle	C₂²×C₉	C₂⁵
Frattini, socle	C₂²×C₃	C₂⁴×D₃
Fitting	D₄²×C₉	C₂
hypercenter	D₄²	D₉
hypocenter	C₉	C₂×D₄²
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ D₄²

3804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 144

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₉×#3498, D₉×#3484, D₄²×AGL(1,ℤ/9), …
maximal normal subgroup of	D₉×#3498, D₉×#3484, D₄²×AGL(1,ℤ/9), …
maximal quotient of	D₉×#2403, D₉×#2433, D₉×#2669, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 136318);