Finite Group Databasebeta

C5×D8×C3⋊C8 #14286072

order1920
automorphism?
homologyAbelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C23

Aliases

direct productC5×D8×C3⋊C8

Splittings

HallC3×C5 ⋊ C8×D8
SylowC3 ⋊ C5×C8×D8

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC3×C4C22×C5×C8
FrattiniC42C22×C5×D3
FittingC3×C4×C5×D8C2
socleC22×C3×C5C4×D4
prime radicalC2×C3×C5×D8C4
cosocleC3×C42C23×C5
hypercenterC4×C5×D8D3
hypocenterC3C5×C8×D8
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C42×C5 ◁ C4×C5×D8

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 11770);