Finite Group Databasebeta

C22×#64784 #12252176

order1280
isoclinismisoclinic class of #3958
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#64784

Splittings

SylowC5 ⋊ C22×#358

Subgroups

subgroupG/H
centerC24#686
commutatorC5×C8C23×C4
FrattiniC2×C8C23×D5
FittingC23×C5×Q16C2
socle, prime radicalC24×C5D8
cosocleC2×C5×C8C24
hypercenterC23×Q16D5
hypocenterC5C22×#358
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8 ◁ C23×Q16

1214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 322444);