Finite Group Databasebeta

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C3×#10604386 #14294818

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

Aliases

direct productC3×#10604386

Splittings

HallC3×C5 ⋊ C2×#344
SylowC5 ⋊ C2×C3×#344

Subgroups

subgroupG/H
centerC3×C4(C2×AGL(1,𝔽5))⋊C4
commutatorC22×C5C2×C3×C42
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC3×C5×#117C4
socleC2×C3×C5C2×#95
prime radicalC23×C3×D5C2×C4
cosocleC22×Dic5C23×C3
hypercenterC3×#117AGL(1,𝔽5)
hypocenterC5C2×C3×#344
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#117

776 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, 20516);