Finite Group Databasebeta

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C3×#10600587 #14305227

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

Aliases

direct productC3×#10600587

Splittings

HallC3×C5 ⋊ #1945
SylowC5 ⋊ C3×#1945

Subgroups

subgroupG/H
centerC2×C3×C4C2×D20
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C4×C5×C8C2
socleC22×C3×C5C4×D4
prime radicalC23×C3×C5#41
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×C4×C8D5
hypocenterC5C3×#1945
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C8 ◁ C2×C3×C4×C8

416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

516 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 30925);