Finite Group Databasebeta

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C3×#10601141 #14301225

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC3×#10601141

Splittings

FittingC3×C5×#419 ⋊ C2
HallC3×C5 ⋊ #1882
SylowC5 ⋊ C3×#1882

Subgroups

subgroupG/H
centerC22×C3#4083
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#419C2
socleC22×C3×C5#120
prime radicalC2×C3×#709C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#419D5
hypocenterC5C3×#1882
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#419

668 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 26923);