Finite Group Databasebeta

← Prev (#14416833) Next (#14416835) →

#137×Dic15 #14416834

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#137×Dic15

Splittings

HallC3×C5 ⋊ C4×#137
SylowC5 ⋊ Dic3×#137
SylowC3 ⋊ Dic5×#137

Subgroups

subgroupG/H
centerC22C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#137C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×#41C22
cosocleC2×C3×C4×C5C24
hypercenterC2×#137D15
hypocenterC3×C5C4×#137
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

968 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142532);