Finite Group Databasebeta

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C2×C3×D3×#120 #11900240

order1152
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C211

Aliases

direct productC2×C3×D3×#120

Splittings

FittingC2×C32×#120 ⋊ C2
SylowC32 ⋊ C22×#120

Subgroups

subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#120C2
socleC23×C32C24
hypercenterC2×C3×#120D3
hypocenterC3C22×C3×#120
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#120

9419 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#120×AGL(1,𝔽7), C2×C3×D3×B(4,𝔽2), C3×D3×#3484, …
maximal normal subgroup ofC2×C3×D3×B(4,𝔽2), C3×D3×#3484, C2×D32×#120
maximal quotient ofD3×#120×AGL(1,𝔽7), C2×C3×D3×B(4,𝔽2), C2×C3×D3×#453, …
automorphism group ofC4×C7×Dic3, C7×C4⋊Dic3, C7×#217, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 134251);