Finite Group Databasebeta

← Prev (#14285481) Next (#14285483) →

C2×C5×#4457 #14285482

order1920
isoclinismisoclinic class of #204
automorphism?
homologyAbelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×C5×#4457

Splittings

HallC3×C5 ⋊ C2×#334
SylowC3 ⋊ C2×C5×#334

Subgroups

subgroupG/H
centerC22×C4×C5D12
commutatorC3×C4C22×C5×C8
FrattiniC42C22×C5×D3
FittingC2×C3×C4×C5×C8C2
socle, prime radicalC23×C3×C5C4⋊C4
cosocleC3×C42C23×C5
hypercenterC2×C4×C5×C8D3
hypocenterC3C2×C5×#334
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4×C5 ◁ C2×C42×C5 ◁ C2×C4×C5×C8

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

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, 11180);