Finite Group Databasebeta

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C2×C3×#65245 #14320276

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×C3×#65245

Splittings

FittingC22×C3×C5×C22⋊C4 ⋊ C2
HallC3×C5 ⋊ C2×#386
SylowC5 ⋊ C2×C3×#386

Subgroups

subgroupG/H
centerC24×C3C22×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC22×C3×C5×C22⋊C4C2
socleC24×C3×C5C23
prime radicalC23×C3×C22⋊D5C2
cosocleC23×C5C24×C3
hypercenterC22×C3×C22⋊C4D5
hypocenterC5C2×C3×#386
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C22×C3×C22⋊C4

3152 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, 45974);