Finite Group Databasebeta

← Prev (#12259302) Next (#12259304) →

C4×#66056 #12259303

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#66056

Splittings

SylowC5 ⋊ C4×Q82

Subgroups

subgroupG/H
centerC22×C4C23×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC4×C5×C4⋊Q8C2
socle, prime radical, cosocleC23×C5C25
hypercenterC4×C4⋊Q8D5
hypocenterC5C4×Q82
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C4×C4⋊Q8

2324 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 329571);