Finite Group Databasebeta

C2×#10617626 #13006144

order1280
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#10617626

Splittings

SylowC5 ⋊ C2×#3458

Subgroups

subgroupG/H
centerC22×C4C23×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC22×C5×#117C2
socleC23×C5C25
prime radicalC25×C5C23
hypercenterC22×#117D5
hypocenterC5C2×#3458
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×#117

7022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1076412);