Finite Group Databasebeta

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C3×#72140 #11784857

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#72140

Splittings

SylowC32 ⋊ #1792

Subgroups

subgroupG/H
centerC22×C3#953
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
Fitting, prime radicalC2×C32×H(5,𝔽2)C2
socleC22×C32#120
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×H(5,𝔽2)D3
hypocenterC3C3×#1792
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×H(5,𝔽2)

1689 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 18868);