Finite Group Databasebeta

C22×C4×#681 #12962688

order1280
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×C4×#681

Splittings

SylowC5 ⋊ C22×C4×M16

Subgroups

subgroupG/H
centerC22×C42C2×D5
commutatorC2×C5C23×C42
FrattiniC2×C4C24×D5
FittingC23×C42×C5C2
socleC24×C5C22×C4
prime radicalC25×C5C2×C4
cosocleC2×C4×C5C25
hypercenterC23×C42D5
hypocenterC5C22×C4×M16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C42 ◁ C23×C42

3950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1032956);