Finite Group Databasebeta

← Prev (#14319381) Next (#14319383) →

C2×C5×Dic3×C22⋊C4 #14319382

order1920
automorphism?
homologyAbelianization (H1) = C22×C42×C5 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C5×Dic3×C22⋊C4

Splittings

HallC3×C5 ⋊ C2×C4×C22⋊C4
SylowC3 ⋊ C2×C4×C5×C22⋊C4

Subgroups

subgroupG/H
centerC24×C5C22×D3
commutatorC2×C3C22×C42×C5
FrattiniC23C23×C5×D3
FittingC22×C3×C5×C22⋊C4C2
socleC24×C3×C5C23
prime radicalC25×C3×C5C22
cosocleC23×C3C24×C5
hypercenterC22×C5×C22⋊C4D3
hypocenterC3C2×C4×C5×C22⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C22×C5×C22⋊C4

2720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45080);