Finite Group Databasebeta

C4×#65892 #12259227

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

Aliases

direct productC4×#65892

Splittings

FittingC42×C5×D4 ⋊ C2
SylowC5 ⋊ C4×#553

Subgroups

subgroupG/H
centerC22×C4C23×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC42×C5×D4C2
socle, cosocleC23×C5C25
prime radicalC2×#65892C2
hypercenterC42×D4D5
hypocenterC5C4×#553
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C42×D4

2600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 329495);