Finite Group Databasebeta

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C22×C3×#833 #11857588

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

Aliases

direct productC22×C3×#833

Splittings

SylowC32 ⋊ C22×#100

Subgroups

subgroupG/H
centerC23×C3#217
commutatorC22×C3C23×C3×C4
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC23×C32×D4C2
socleC23×C32C22⋊C4
cosocleC2×C3×C4C24×C3
hypercenterC23×C3×D4D3
hypocenterC3C22×C3×#100
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C23×C3×D4

2665 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 91599);