Finite Group Databasebeta

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C3×#10610437 #14412199

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC3×#10610437

Splittings

FittingC2×C3×C5×#101 ⋊ C2
HallC3×C5 ⋊ #2889
SylowC5 ⋊ C3×#2889

Subgroups

subgroupG/H
centerC2×C3C2×D5×C22⋊C4
commutatorC22×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#101C2
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×C3×#4147C2
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×#101D5
hypocenterC5C3×#2889
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×#101

1408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137897);