Finite Group Databasebeta

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C3×#10600324 #14283260

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

Aliases

direct productC3×#10600324

Splittings

FittingC3×C5×#381 ⋊ C2
HallC3×C5 ⋊ #1510
SylowC5 ⋊ C3×#1510

Subgroups

subgroupG/H
centerC22×C3C2×#685
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#381C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#4076C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#381D5
hypocenterC5C3×#1510
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#381

652 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

246 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 8958);