Finite Group Databasebeta

C2×C3×#65725 #14478122

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×C3×#65725

Splittings

HallC3×C5 ⋊ C2×#504
SylowC5 ⋊ C2×C3×#504

Subgroups

subgroupG/H
centerC2×C3×C4C22×AGL(1,𝔽5)
commutatorC2×C5C23×C3×C8
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC2×C3×C5×M16C4
socleC22×C3×C5C22×C8
prime radicalC2×C3×#709C4
cosocle#168C24×C3
hypercenterC2×C3×M16AGL(1,𝔽5)
hypocenterC5C2×C3×#504
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×M16

736 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 203820);