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C3×#10599507 #14309022

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

Aliases

direct productC3×#10599507

Splittings

FittingC3×C5×H(3,ℤ/4) ⋊ C2
HallC3×C5 ⋊ #2031
SylowC5 ⋊ C3×#2031

Subgroups

subgroupG/H
centerC3×C4#4021
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×H(3,ℤ/4)C2
socleC2×C3×C5#393
prime radicalC2×C3×#709C22
hypercenterC3×H(3,ℤ/4)D5
hypocenterC5C3×#2031
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×H(3,ℤ/4)

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

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, 34720);