Finite Group Databasebeta

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C2×C3×#65279 #14320442

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C3×#65279

Splittings

FittingC22×C3×C5×C4⋊C4 ⋊ C2
HallC3×C5 ⋊ C2×#388
SylowC5 ⋊ C2×C3×#388

Subgroups

subgroupG/H
centerC24×C3C22×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC22×C3×C5×C4⋊C4C2
socleC24×C3×C5C23
prime radicalC24×C3×D5C22
cosocleC23×C5C24×C3
hypercenterC22×C3×C4⋊C4D5
hypocenterC5C2×C3×#388
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C22×C3×C4⋊C4

1856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 46140);