Finite Group Databasebeta

C22×#64722 #12251925

order1280
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#64722

Splittings

SylowC5 ⋊ C22×#346

Subgroups

subgroupG/H
centerC23×C8C2×D5
commutatorC2×C5C22×C4×C8
FrattiniC2×C8C23×D5
FittingC23×C5×C16C2
socle, prime radicalC24×C5C2×C8
cosocleC2×C5×C8C24
hypercenterC23×C16D5
hypocenterC5C22×#346
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C8 ◁ C23×C16

942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

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, 322193);