Finite Group Databasebeta

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C2×D9×#120 #11900238

order1152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productC2×D9×#120

Splittings

FittingC2×C9×#120 ⋊ C2
SylowC9 ⋊ C22×#120

Subgroups

subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#120C2
socleC23×C3C23×D3
hypercenterC2×#120D9
hypocenterC9C22×#120
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#120

6816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD9×#3484, C2×#120×AGL(1,ℤ/9), C2×D9×B(4,𝔽2), …
maximal normal subgroup ofD9×#3484, C2×#120×AGL(1,ℤ/9), C2×D9×B(4,𝔽2), …
maximal quotient ofC2×D9×#453, C2×D9×B(4,𝔽2), D9×#2403, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 134249);