Finite Group Databasebeta

← Prev (#14320360) Next (#14320362) →

C2×#11752370 #14320361

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#11752370
unambiguous semidirect productD5⋊#4980

Splittings

FittingC2×C3×C5×C4⋊C4 ⋊ C4
HallC3×C5 ⋊ C2×#387
SylowC5 ⋊ C2×#4980
SylowC3 ⋊ C2×#65711

Subgroups

subgroupG/H
centerC23C22×ΓL(1,𝔽16)
commutatorC22×C3×C5C23×C4
FrattiniC22C23×ΓL(1,𝔽16)
FittingC2×C3×C5×C4⋊C4C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC2×C4⋊C4ΓL(1,𝔽16)
hypocenterC3×C5C2×#387
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

1424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 46059);