Finite Group Databasebeta

C3×#10615628 #14416551

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

Aliases

direct productC3×#10615628

Splittings

HallC3×C5 ⋊ #2943
SylowC5 ⋊ C3×#2943

Subgroups

subgroupG/H
centerC2×C3×C4D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
Fitting, prime radicalC2×C3×C5×#135C2
socleC22×C3×C5C22×D4
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×#135D5
hypocenterC5C3×#2943
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#135

984 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, 142249);