Finite Group Databasebeta

C2×C5×#5196 #14417839

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC2×C5×#5196

Splittings

HallC3×C5 ⋊ C2×#443
SylowC3 ⋊ C2×C5×#443

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
Fitting, prime radicalC2×C3×C5×#135C2
socleC22×C3×C5C4×D4
cosocleC2×C3×C4C24×C5
hypercenterC2×C5×#135D3
hypocenterC3C2×C5×#443
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C2×C5×#135

944 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, 143537);