Finite Group Databasebeta

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C3×#10604220 #14302047

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

Aliases

direct productC3×#10604220

Splittings

FittingC2×C3×C5×C22⋊C4 ⋊ C4
HallC3×C5 ⋊ #1898
SylowC5 ⋊ C3×#1898

Subgroups

subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C22⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#4028C2
cosocleC23×D5C23×C3
hypercenterC2×C3×C22⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1898
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C2×C3×C22⋊C4

1196 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, 27745);