Finite Group Databasebeta

← Prev (#14285681) Next (#14285683) →

C3×#10600524 #14285682

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

Aliases

direct productC3×#10600524

Splittings

HallC3×C5 ⋊ #1567
SylowC5 ⋊ C3×#1567

Subgroups

subgroupG/H
centerC2×C3×C4C2×D20
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC2×C3×C4×C5×C8C2
socleC22×C3×C5C2×C4⋊C4
prime radicalC23×C3×C5C4⋊C4
cosocleC42×C5C23×C3
hypercenterC2×C3×C4×C8D5
hypocenterC5C3×#1567
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×C4×C8

368 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, 11380);