Finite Group Databasebeta

C2×M16×D20 #12963203

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×M16×D20

Splittings

FittingC2×C4×C5×M16 ⋊ C2
SylowC5 ⋊ C2×D4×M16

Subgroups

subgroupG/H
centerC22×C4C23×D5
commutatorC22×C5C24×C4
FrattiniC2×C4C24×D5
FittingC2×C4×C5×M16C2
socleC23×C5C23×C4
prime radicalC23×D20C4
cosocleC2×C4×C5C25
hypercenterC2×C4×M16D5
hypocenterC5C2×D4×M16
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C4×M16

3218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1033471);