Finite Group Databasebeta

C2×C5×#5221 #14320775

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C5×#5221

Splittings

HallC3×C5 ⋊ C2×#390
SylowC3 ⋊ C2×C5×#390

Subgroups

subgroupG/H
centerC24×C5C22×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
Fitting, prime radicalC23×C3×C5×D4C2
socleC24×C3×C5C23
cosocleC23×C3C24×C5
hypercenterC23×C5×D4D3
hypocenterC3C2×C5×#390
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C23×C5×D4

2720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 46473);