Finite Group Databasebeta

← Prev (#14425302) Next (#14425304) →

C3×#10615835 #14425303

order1920
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC3×#10615835

Splittings

FittingC2×C3×C5×H(5,𝔽2) ⋊ C2
HallC3×C5 ⋊ #3019
SylowC5 ⋊ C3×#3019

Subgroups

subgroupG/H
centerC2×C3C2×#4099
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×H(5,𝔽2)C2
socleC2×C3×C5C2×#120
hypercenterC2×C3×H(5,𝔽2)D5
hypocenterC5C3×#3019
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×H(5,𝔽2)

1524 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 151001);