Finite Group Databasebeta

C2×C3×#65787 #14411693

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×#65787

Splittings

HallC3×C5 ⋊ C2×#408
SylowC5 ⋊ C2×C3×#408

Subgroups

subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC22×C3×C5×Q8C4
socleC23×C3×C5C22×C4
prime radicalC22×C3×#713C2
cosocleC2×Dic5C24×C3
hypercenterC22×C3×Q8AGL(1,𝔽5)
hypocenterC5C2×C3×#408
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×Q8

1584 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137391);