Finite Group Databasebeta

← Prev (#14411927) Next (#14411929) →

C2×C3×#65785 #14411928

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C3×#65785

Splittings

FittingC22×C3×C5×Q8 ⋊ C4
HallC3×C5 ⋊ C2×#410
SylowC5 ⋊ C2×C3×#410

Subgroups

subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC22×C3×C5×Q8C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×#713C2
cosocleC22×D5C24×C3
hypercenterC22×C3×Q8AGL(1,𝔽5)
hypocenterC5C2×C3×#410
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×Q8

1576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 137626);