Finite Group Databasebeta

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C3×#10600561 #14304558

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

Aliases

direct productC3×#10600561

Splittings

FittingC2×C3×C4×C5×C8 ⋊ C2
HallC3×C5 ⋊ #1934
SylowC5 ⋊ C3×#1934

Subgroups

subgroupG/H
centerC23×C3C2×D20
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C4×C5×C8C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×C4×C8D5
hypocenterC5C3×#1934
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4×C8

584 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 30256);