Finite Group Databasebeta

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C3×#10605400 #14332543

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

Aliases

direct productC3×#10605400

Splittings

HallC3×C5 ⋊ #2399
SylowC5 ⋊ C3×#2399

Subgroups

subgroupG/H
centerC22×C3×C4C22×D5
commutator, cosocleC23×C5C24×C3
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C4⋊C4C2
socle, prime radicalC23×C3×C5C24
hypercenterC3×C4×C4⋊C4D5
hypocenterC5C3×#2399
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C4⋊C4

1008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 58241);