Finite Group Databasebeta

← Prev (#13028071) Next (#13028073) →

C2×#10604345 #13028072

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#10604345
unambiguous semidirect productD5⋊#1445

Splittings

FittingC22×C5×C4⋊C4 ⋊ C4
SylowC5 ⋊ C2×#1445

Subgroups

subgroupG/H
centerC24C22×AGL(1,𝔽5)
commutatorC23×C5C23×C4
FrattiniC23C23×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC24×C5C22×C4
prime radicalC24×D5C23
cosocleC23×D5C24
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5C2×#1445
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C4⋊C4

2942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1098340);