Finite Group Databasebeta

C2×C5×#5232 #14412479

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

Aliases

direct productC2×C5×#5232

Splittings

HallC3×C5 ⋊ C2×#417
SylowC3 ⋊ C2×C5×#417

Subgroups

subgroupG/H
centerC23×C5C2×#67
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
Fitting, prime radicalC22×C3×C5×#41C2
socleC23×C3×C5C2×D4
cosocleC2×C3×C4C24×C5
hypercenterC22×C5×#41D3
hypocenterC3C2×C5×#417
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ C22×C5×#41

1632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 138177);