Finite Group Databasebeta

← Prev (#14313994) Next (#14313996) →

C3×D5×#359 #14313995

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

Aliases

direct productC3×D5×#359

Splittings

FittingC3×C5×#359 ⋊ C2
HallC3×C5 ⋊ C2×#359
SylowC5 ⋊ C2×C3×#359

Subgroups

subgroupG/H
centerC3×C4D5×D8
commutatorC5×C8C22×C3×C4
FrattiniC2×C8C22×C3×D5
FittingC3×C5×#359C2
socleC2×C3×C5C2×#102
prime radicalC3×D5×#135C2
cosocleC2×C5×C8C23×C3
hypercenterC3×#359D5
hypocenterC5C2×C3×#359
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#359

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 39693);