Finite Group Databasebeta

C2×#10598171 #11989440

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

Aliases

direct productC2×#10598171

Splittings

SylowC5 ⋊ C2×#1298

Subgroups

subgroupG/H
centerC22×C4#685
commutatorC2×C4×C5C2×C42
FrattiniC23×C4C22×D5
FittingC22×C5×C22⋊C8C2
socleC23×C5#95
prime radicalC25×C5Q8
cosocleC23×C4×C5C23
hypercenterC22×C22⋊C8D5
hypocenterC5C2×#1298
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C22×C22⋊C8

938 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 59708);