Finite Group Databasebeta

C2×#10598250 #11989701

order1280
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#10598250

Splittings

SylowC5 ⋊ C2×#1308

Subgroups

subgroupG/H
centerC23#3963
commutatorC23×C5C2×C42
FrattiniC2×C42C22×D5
FittingC2×C5×#432C2
socleC23×C5#95
prime radicalC24×C5C42
cosocleC2×C42×C5C23
hypercenterC2×#432D5
hypocenterC5C2×#1308
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 59969);