Finite Group Databasebeta

C4×#65277 #12020489

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C42

Aliases

direct productC4×#65277

Splittings

FittingC2×C4×C5×C4⋊C4 ⋊ C2
SylowC5 ⋊ C4×#390

Subgroups

subgroupG/H
centerC23×C4C22×D5
commutatorC22×C5C22×C42
FrattiniC24C23×D5
FittingC2×C4×C5×C4⋊C4C2
socle, cosocleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×C4×C4⋊C4D5
hypocenterC5C4×#390
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

2894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 90757);