Finite Group Databasebeta

C4×#65906 #12257549

order1280
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#65906

Splittings

FittingC42×C5×Q8 ⋊ C2
SylowC5 ⋊ C4×#519

Subgroups

subgroupG/H
centerC22×C4C23×D5
commutatorC2×C5C23×C42
FrattiniC23C24×D5
FittingC42×C5×Q8C2
socle, cosocleC23×C5C25
prime radicalC23×D5C24
hypercenterC42×Q8D5
hypocenterC5C4×#519
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C42×Q8

3402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 327817);