Finite Group Databasebeta

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C3×#10598586 #14277177

order1920
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C23

Aliases

direct productC3×#10598586

Splittings

FittingC3×C5×C4⋊C8 ⋊ C4
HallC3×C5 ⋊ #1296
SylowC5 ⋊ C3×#1296

Subgroups

subgroupG/H
centerC22×C3(C2×AGL(1,𝔽5))⋊C4
commutatorC2×C4×C5C3×C42
FrattiniC42C2×C3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C8C4
socleC22×C3×C5#95
prime radicalC22×C3×D5C22⋊C4
cosocleC42×D5C22×C3
hypercenterC3×C4⋊C8AGL(1,𝔽5)
hypocenterC5C3×#1296
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4⋊C8

376 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 2875);