Finite Group Databasebeta

C3×#10598190 #14279131

order1920
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C22

Aliases

direct productC3×#10598190

Splittings

HallC3×C5 ⋊ #1394
SylowC5 ⋊ C3×#1394

Subgroups

subgroupG/H
centerC22×C3#3938
commutatorC2×C4×C5C3×C42
FrattiniC22×Q8C2×C3×D5
FittingC2×C3×C5×#101C2
socleC22×C3×C5#99
prime radicalC23×C3×C5C22⋊C4
cosocleC22×C5×Q8C22×C3
hypercenterC2×C3×#101D5
hypocenterC5C3×#1394
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×Q8 ◁ C2×C3×#101

344 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4829);