Finite Group Databasebeta

C2×C5×#4527 #14294683

order1920
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C25

Aliases

direct productC2×C5×#4527

Splittings

HallC3×C5 ⋊ C2×#342
SylowC3 ⋊ C2×C5×#342

Subgroups

subgroupG/H
centerC23×C5(C2×D3)⋊C4
commutatorC22×C3C2×C42×C5
FrattiniC24C22×C5×D3
FittingC22×C3×C5×C22⋊C4C2
socleC23×C3×C5C22⋊C4
prime radicalC25×C3×C5C22
cosocleC24×C3C23×C5
hypercenterC22×C5×C22⋊C4D3
hypocenterC3C2×C5×#342
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C25×C5 ◁ C22×C5×C22⋊C4

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20381);