Finite Group Databasebeta

C2×#10598211 #12014200

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

Aliases

direct productC2×#10598211

Splittings

SylowC5 ⋊ C2×#1383

Subgroups

subgroupG/H
centerC23#3940
commutatorC5×C8C2×C42
FrattiniC22×C8C22×D5
FittingC22×C5×#106C2
socleC23×C5#106
prime radicalC24×C5SD16
cosocleC22×C5×C8C23
hypercenterC22×#106D5
hypocenterC5C2×#1383
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#106

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 84468);