Finite Group Databasebeta

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C3×#10604343 #14279963

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC3×#10604343

Splittings

FittingC2×C3×C5×C4⋊C4 ⋊ C4
HallC3×C5 ⋊ #1436
SylowC5 ⋊ C3×#1436

Subgroups

subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC22×C5C2×C3×C42
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C4⋊C4C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C23
cosocleC23×D5C23×C3
hypercenterC2×C3×C4⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1436
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C4⋊C4

1224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 5661);