Finite Group Databasebeta

C2×C3×#65850 #14479012

order1920
automorphism?
homologyAbelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C3×#65850

Splittings

HallC3×C5 ⋊ C2×#519
SylowC5 ⋊ C2×C3×#519

Subgroups

subgroupG/H
centerC23×C3C23×D5
commutatorC2×C5C24×C3×C4
FrattiniC22C24×C3×D5
FittingC2×C3×C5×#117C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC22×C5C25×C3
hypercenterC2×C3×#117D5
hypocenterC5C2×C3×#519
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#117

2976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204710);