Finite Group Databasebeta

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C3×#10604201 #14280861

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C24

Aliases

direct productC3×#10604201

Splittings

HallC3×C5 ⋊ #1459
SylowC5 ⋊ C3×#1459

Subgroups

subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C22×C3×C8
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C22⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C22⋊D5C4
cosocleC22×Dic5C23×C3
hypercenterC2×C3×C22⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1459
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C2×C3×C22⋊C4

664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 6559);