Finite Group Databasebeta

C2×#10605143 #12257520

order1280
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#10605143

Splittings

FittingC2×C5×#376 ⋊ C2
SylowC5 ⋊ C2×#2275

Subgroups

subgroupG/H
centerC24C23×D5
commutatorC2×C5C23×C42
FrattiniC23C24×D5
FittingC2×C5×#376C2
socleC24×C5C24
prime radicalC23×D20C22
cosocleC23×C5C25
hypercenterC2×#376D5
hypocenterC5C2×#2275
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#376

4694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

296 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 327788);