Finite Group Databasebeta

C3×C4×#4023 #14319481

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC3×C4×#4023

Splittings

HallC3×C5 ⋊ C4×#117
SylowC5 ⋊ C3×C4×#117

Subgroups

subgroupG/H
centerC22×C3×C4C22×D5
commutatorC2×C5C22×C3×C42
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C5C24×C3
hypercenterC3×C4×C22⋊C4D5
hypocenterC5C3×C4×#117
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C22⋊C4

1504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45179);