Finite Group Databasebeta

C42×#687 #12097770

order1280
isoclinismisoclinic class of #686
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC42×#687

Splittings

SylowC5 ⋊ C42×SD16

Subgroups

subgroupG/H
centerC2×C42C22⋊D5
commutatorC4×C5C22×C42
FrattiniC22×C4C23×D5
FittingC42×C5×D4C2
socleC23×C5C22×D4
prime radicalC22×C5×D4C23
cosocleC22×C4×C5C24
hypercenterC42×D4D5
hypocenterC5C42×SD16
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×D4

1230 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, 168038);