Finite Group Databasebeta

C2×D4×#672 #12252450

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

Aliases

direct productC2×D4×#672

Splittings

SylowC5 ⋊ C2×D4×C16

Subgroups

subgroupG/H
centerC22×C8C22×D5
commutatorC2×C5C23×C16
FrattiniC2×C8C23×D5
FittingC2×C5×C8×D4C2
socleC23×C5C22×C8
prime radicalC22×C5×D4C8
cosocleC2×C5×C8C24
hypercenterC2×C8×D4D5
hypocenterC5C2×D4×C16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C8 ◁ C2×C8×D4

806 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, 322718);