Finite Group Databasebeta

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C3×#10604089 #14296471

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

Aliases

direct productC3×#10604089

Splittings

FittingC3×C5×#108 ⋊ C4
HallC3×C5 ⋊ #1772
SylowC5 ⋊ C3×#1772

Subgroups

subgroupG/H
centerC3×C4D4×AGL(1,𝔽5)
commutatorC4×C5C2×C3×C42
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#108C4
socleC2×C3×C5C4×C4⋊C4
prime radicalC22×C3×D5#41
cosocleC2×C4×D5C23×C3
hypercenterC3×#108AGL(1,𝔽5)
hypocenterC5C3×#1772
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×#108

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 22169);