Finite Group Databasebeta

C3×#10601635 #14286594

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×#10601635

Splittings

HallC3×C5 ⋊ #1582
SylowC5 ⋊ C3×#1582

Subgroups

subgroupG/H
centerC2×C3×C4C2×C22⋊D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×C8×D4C2
socleC22×C3×C5C4×D4
prime radicalC2×C3×C5×D4C2×C4
cosocleC42×C5C23×C3
hypercenterC3×C8×D4D5
hypocenterC5C3×#1582
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×C8 ◁ C3×C8×D4

336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 12292);