Finite Group Databasebeta

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C3×#10599392 #14294995

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC3×#10599392

Splittings

FittingC3×C5×#336 ⋊ C2
HallC3×C5 ⋊ C4×C22⋊C8
SylowC5 ⋊ C3×C4×C22⋊C8

Subgroups

subgroupG/H
centerC22×C3×C4C22×D5
commutatorC2×C5C2×C3×C4×C8
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#336C2
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C4×C5C23×C3
hypercenterC3×#336D5
hypocenterC5C3×C4×C22⋊C8
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C3×#336

872 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20693);