Finite Group Databasebeta

C3×D5⋊#504 #14478124

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

Aliases

direct productC3×D5⋊#504
unambiguous semidirect productD5⋊(C3×#504)

Splittings

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

Subgroups

subgroupG/H
centerC3×C8C22×AGL(1,𝔽5)
commutatorC2×C5C23×C3×C8
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC3×C5×#131C4
socleC2×C3×C5C23×C8
prime radicalC3×D5×#41C4
cosocle#168C24×C3
hypercenterC3×#131AGL(1,𝔽5)
hypocenterC5C2×C3×#504
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C8 ◁ C3×#131

736 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 203822);