Finite Group Databasebeta

← Prev (#14294688) Next (#14294690) →

C2×C3×#64866 #14294689

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

Aliases

direct productC2×C3×#64866

Splittings

FittingC2×C3×C5×C22⋊C4 ⋊ C4
HallC3×C5 ⋊ C2×#342
SylowC5 ⋊ C2×C3×#342

Subgroups

subgroupG/H
centerC22×C3(C2×AGL(1,𝔽5))⋊C4
commutatorC22×C5C2×C3×C42
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C22⋊C4C4
socleC22×C3×C5#95
prime radicalC24×C3×D5C22
cosocleC23×D5C23×C3
hypercenterC2×C3×C22⋊C4AGL(1,𝔽5)
hypocenterC5C2×C3×#342
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C2×C3×C22⋊C4

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20387);