Finite Group Databasebeta

C3×#10600591 #14284184

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#10600591

Splittings

FittingC2×C3×C5×#97 ⋊ C2
HallC3×C5 ⋊ #1530
SylowC5 ⋊ C3×#1530

Subgroups

subgroupG/H
centerC22×C3C2×#685
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC2×C3×C5×#97C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#65811C2
cosocleC42×C5C23×C3
hypercenterC2×C3×#97D5
hypocenterC5C3×#1530
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C2×C3×#97

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 9882);