Finite Group Databasebeta

C3×#10615523 #14418015

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

Aliases

direct productC3×#10615523

Splittings

FittingC2×C3×C5×#131 ⋊ C2
HallC3×C5 ⋊ #2955
SylowC5 ⋊ C3×#2955

Subgroups

subgroupG/H
centerC3×C8C2×C22⋊D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#131C2
socleC2×C3×C5C2×C4×D4
prime radicalC3×#66156C2
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×#131D5
hypocenterC5C3×#2955
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C8 ◁ C22×C3×C8 ◁ C2×C3×#131

912 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 143713);