Finite Group Databasebeta

C2×C3×#65761 #14412109

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

Aliases

direct productC2×C3×#65761

Splittings

HallC3×C5 ⋊ C2×#413
SylowC5 ⋊ C2×C3×#413

Subgroups

subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC23×C3×C4×C5C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×#709C2
cosocleC2×Dic5C24×C3
hypercenterC23×C3×C4AGL(1,𝔽5)
hypocenterC5C2×C3×#413
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C23×C3×C4

1512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 137807);