Finite Group Databasebeta

C2×C16×C22⋊D5 #12252448

order1280
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productC2×C16×C22⋊D5

Splittings

FittingC23×C5×C16 ⋊ C2
SylowC5 ⋊ C2×D4×C16

Subgroups

subgroupG/H
centerC22×C16C2×D5
commutatorC2×C5C23×C16
FrattiniC2×C8C23×D5
FittingC23×C5×C16C2
socleC23×C5C22×C8
prime radicalC22×C22⋊D5C8
cosocleC2×C5×C8C24
hypercenterC23×C16D5
hypocenterC5C2×D4×C16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C16 ◁ C23×C16

806 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, 322716);