Finite Group Databasebeta

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C3×#10604799 #14301024

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#10604799

Splittings

FittingC2×C3×C5×D8 ⋊ C4
HallC3×C5 ⋊ #1879
SylowC5 ⋊ C3×#1879

Subgroups

subgroupG/H
centerC22×C3D4×AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×D8C4
socleC22×C3×C5C4×D4
prime radicalC2×C3×D5×D8C2
cosocleC2×C4×D5C23×C3
hypercenterC2×C3×D8AGL(1,𝔽5)
hypocenterC5C3×#1879
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D8

876 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 26722);