Finite Group Databasebeta

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C3×#10604255 #14280102

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC3×#10604255

Splittings

FittingC2×C3×C5×C22⋊C4 ⋊ C4
HallC3×C5 ⋊ #1440
SylowC5 ⋊ C3×#1440

Subgroups

subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C22⋊C4C4
socleC23×C3×C5C22×C4
prime radicalC24×C3×D5C22
cosocleC23×D5C23×C3
hypercenterC2×C3×C22⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1440
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊C4

1472 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, 5800);