Finite Group Databasebeta

← Prev (#14280771) Next (#14280773) →

C2×C3×#64748 #14280772

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C3×#64748

Splittings

HallC3×C5 ⋊ C2×#324
SylowC5 ⋊ C2×C3×#324

Subgroups

subgroupG/H
centerC23×C3C22⋊Dic5
commutatorC22×C5C22×C3×C8
FrattiniC22×C4C22×C3×D5
FittingC22×C3×C5×C4⋊C4C2
socleC23×C3×C5C22⋊C4
prime radicalC24×C3×C5C2×C4
cosocleC22×C4×C5C23×C3
hypercenterC22×C3×C4⋊C4D5
hypocenterC5C2×C3×#324
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C22×C3×C4⋊C4

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 6470);