Finite Group Databasebeta

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C2×C3×D3×#100 #11857582

order1152
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×D3×#100

Splittings

FittingC2×C32×#100 ⋊ C2
SylowC32 ⋊ C22×#100

Subgroups

subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC22×C3C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#100C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3×D4C2
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×#100D3
hypocenterC3C22×C3×#100
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#100

2077 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×D3×#453, D3×#100×AGL(1,𝔽7), C2×#100×AGL(1,ℤ/9), …
maximal normal subgroup ofC2×C3×D3×#453, C2×D32×#100, C2×D3×#4747
maximal quotient ofD3×#100×AGL(1,𝔽7), C2×#100×AGL(1,ℤ/9), C2×C3×#10591503

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 91593);