Finite Group Databasebeta

C2×M16×#168 #12064872

order1280
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M16×#168

Splittings

SylowC5 ⋊ C2×C8×M16

Subgroups

subgroupG/H
centerC2×C42C22×D5
commutatorC2×C5C22×C4×C8
FrattiniC42C23×D5
FittingC2×C4×C5×M16C2
socleC23×C5C2×C42
prime radicalC24×C5C42
cosocleC42×C5C24
hypercenterC2×C4×M16D5
hypocenterC5C2×C8×M16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

1046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 135140);