Finite Group Databasebeta

C22×C4×#685 #12257474

order1280
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4

Aliases

direct productC22×C4×#685

Splittings

FittingC23×C42×C5 ⋊ C2
SylowC5 ⋊ C22×C4×C22⋊C4

Subgroups

subgroupG/H
centerC24×C4C2×D5
commutatorC2×C5C23×C42
FrattiniC23C24×D5
FittingC23×C42×C5C2
socleC25×C5C23
prime radicalC25×D5C22
cosocleC23×C5C25
hypercenterC23×C42D5
hypocenterC5C22×C4×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C24×C4 ◁ C23×C42

9534 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, 327742);