Finite Group Databasebeta

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C3×#10604346 #14282826

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#10604346

Splittings

FittingC3×C5×#117 ⋊ C4
HallC3×C5 ⋊ #1501
SylowC5 ⋊ C3×#1501

Subgroups

subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#117C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#65858C2
cosocleC2×C4×D5C23×C3
hypercenterC3×#117AGL(1,𝔽5)
hypocenterC5C3×#1501
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C3×#117

608 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, 8524);