Finite Group Databasebeta

C4×C5×#926 #14319489

order1920
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C42×C5 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×C5×#926

Splittings

HallC3×C5 ⋊ C4×#117
SylowC3 ⋊ C4×C5×#117

Subgroups

subgroupG/H
centerC2×C42×C5C2×D3
commutatorC2×C3C22×C42×C5
FrattiniC23C23×C5×D3
FittingC22×C3×C42×C5C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C3C24×C5
hypercenterC22×C42×C5D3
hypocenterC3C4×C5×#117
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C42×C5 ◁ C22×C42×C5

1504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45187);