Finite Group Databasebeta

C2×C4×#4053 #12962705

order1280
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×#4053

Splittings

FittingC2×C4×C5×M16 ⋊ C2
SylowC5 ⋊ C2×C4×#131

Subgroups

subgroupG/H
centerC2×C42C22×D5
commutatorC2×C5C23×C42
FrattiniC2×C4C24×D5
FittingC2×C4×C5×M16C2
socleC23×C5C23×C4
prime radicalC22×#709C22
cosocleC2×C4×C5C25
hypercenterC2×C4×M16D5
hypocenterC5C2×C4×#131
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

3366 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, 1032973);