Finite Group Databasebeta

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C3×#10599806 #14298761

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×#10599806

Splittings

HallC3×C5 ⋊ #1833
SylowC5 ⋊ C3×#1833

Subgroups

subgroupG/H
centerC3×C4#4023
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#344C2
socleC2×C3×C5#382
prime radicalC23×C3×C5#41
cosocleC22×C4×C5C23×C3
hypercenterC3×#344D5
hypocenterC5C3×#1833
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#344

344 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, 24459);