Finite Group Databasebeta

C2×#10598176 #11989631

order1280
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#10598176

Splittings

SylowC5 ⋊ C2×#1305

Subgroups

subgroupG/H
centerC23#3963
commutatorC23×C5C2×C42
FrattiniC23×C4C22×D5
FittingC2×C5×#407C2
socleC23×C5#95
prime radicalC25×C5C2×C4
cosocleC23×C4×C5C23
hypercenterC2×#407D5
hypocenterC5C2×#1305
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

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, 59899);