Finite Group Databasebeta

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C3×#10617506 #14322389

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C27

Aliases

direct productC3×#10617506

Splittings

FittingC22×C3×C5×D4 ⋊ C4
HallC3×C5 ⋊ #2308
SylowC5 ⋊ C3×#2308

Subgroups

subgroupG/H
centerC22×C3C23×AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC22×C3×C5×D4C4
socleC22×C3×C5C23×C4
prime radicalC22×C3×D4×D5C2
cosocleC22×D5C24×C3
hypercenterC22×C3×D4AGL(1,𝔽5)
hypocenterC5C3×#2308
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×D4

2320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 48087);