Finite Group Databasebeta

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C3×#10604461 #14301624

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#10604461

Splittings

FittingC3×C5×#120 ⋊ C4
HallC3×C5 ⋊ #1889
SylowC5 ⋊ C3×#1889

Subgroups

subgroupG/H
centerC2×C3#65779
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC3×C5×#120C4
socleC2×C3×C5#386
prime radicalC3×D5×#120C2
cosocleC23×D5C23×C3
hypercenterC3×#120AGL(1,𝔽5)
hypocenterC5C3×#1889
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C3×#120

1156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽5)×B(4,𝔽2), D3×#10604461, #72229597
maximal normal subgroup ofC3×AGL(1,𝔽5)×B(4,𝔽2), D3×#10604461, #72229597

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 27322);