Finite Group Databasebeta

← Prev (#14511001) Next (#14511003) →

C5×A4×SD32 #14511002

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×A4×SD32
unambiguous semidirect product(C22×SD32)⋊(C3×C5)
unambiguous semidirect product(C22×C5×SD32)⋊C3

Splittings

Fitting, HallC22×C5×SD32 ⋊ C3
SylowC22×SD32 ⋊ C3×C5

Subgroups

subgroupG/H
centerC2×C5A4×D8
commutator, cosocleC22×C8C22×C3×C5
FrattiniC8C22×C5×A4
FittingC22×C5×SD32C3
socleC23×C5C3×D8
prime radicalC5×A4×D8C2
hypercenterC5×SD32A4
hypocenterC22C3×C5×SD32
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C23 ▷ C22
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×C8 ◁ C5×SD32

220 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236700);