Finite Group Databasebeta

C5×D4×#217 #14325910

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C27

Aliases

direct productC5×D4×#217

Splittings

HallC3×C5 ⋊ D4×C22⋊C4
SylowC3 ⋊ C5×D4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
Fitting, prime radicalC23×C3×C5×D4C2
socleC23×C3×C5C24
cosocleC23×C3C24×C5
hypercenterC23×C5×D4D3
hypocenterC3C5×D4×C22⋊C4
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C23×C5×D4

2504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 51608);