Finite Group Databasebeta

C3×#10602404 #14300473

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC3×#10602404

Splittings

HallC3×C5 ⋊ #1870
SylowC5 ⋊ C3×#1870

Subgroups

subgroupG/H
centerC22×C3×C4C22×D5
commutatorC23×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C22×C4
prime radicalC22×C3×C5×D4C4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×C4×D4D5
hypocenterC5C3×#1870
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4×D4

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 26171);