Finite Group Databasebeta

← Prev (#14295481) Next (#14295483) →

Dic5×#824 #14295482

order1920
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productDic5×#824

Splittings

HallC3×C5 ⋊ C4×#101
SylowC5 ⋊ C4×#824
SylowC3 ⋊ Dic5×#101

Subgroups

subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC22×C3×C5C2×C42
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5C4×#101
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21180);