Finite Group Databasebeta

← Prev (#14286094) Next (#14286096) →

#168×#213 #14286095

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

Aliases

direct product#168×#213

Splittings

HallC3×C5 ⋊ C8×D8
SylowC5 ⋊ C8×#213
SylowC3 ⋊ D8×#168

Subgroups

subgroupG/H
centerC2×C4D5×#67
commutatorC3×C4×C5C22×C8
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C4×D4
prime radicalC2×C5×#213C4
cosocleC3×C42×C5C23
hypercenterC4×D4D3×D5
hypocenterC3×C5C8×D8
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 11793);