Finite Group Databasebeta

C2×C3×#64747 #14294684

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×C3×#64747

Splittings

HallC3×C5 ⋊ C2×#342
SylowC5 ⋊ C2×C3×#342

Subgroups

subgroupG/H
centerC23×C3#685
commutatorC22×C5C2×C3×C42
FrattiniC24C22×C3×D5
FittingC22×C3×C5×C22⋊C4C2
socleC23×C3×C5C22⋊C4
prime radicalC25×C3×C5C22
cosocleC24×C5C23×C3
hypercenterC22×C3×C22⋊C4D5
hypocenterC5C2×C3×#342
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C25×C3 ◁ C22×C3×C22⋊C4

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20382);