Finite Group Databasebeta

C5×D4×C3⋊C16 #14314976

order1920
automorphism?
homologyAbelianization (H1) = C22×C5×C16 · Schur multiplier (H2) = C23

Aliases

direct productC5×D4×C3⋊C16

Splittings

HallC3×C5 ⋊ D4×C16
SylowC3 ⋊ C5×D4×C16

Subgroups

subgroupG/H
centerC2×C5×C8C22×D3
commutatorC2×C3C22×C5×C16
FrattiniC2×C8C22×C5×D3
FittingC3×C5×C8×D4C2
socleC22×C3×C5C22×C8
prime radicalC2×C3×C5×D4C8
cosocleC2×C3×C8C23×C5
hypercenterC5×C8×D4D3
hypocenterC3C5×D4×C16
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5×C8 ◁ C5×C8×D4

348 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, 40674);