Finite Group Databasebeta

C2×C22⋊#3926 #12019491

order1280
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊#3926

Splittings

SylowC5 ⋊ C2×C22⋊C32

Subgroups

subgroupG/H
centerC22×C16C2×D5
commutatorC2×C5C22×C32
FrattiniC2×C16C22×D5
FittingC23×C5×C16C2
socleC23×C5C2×C16
prime radicalC24×C5C16
cosocleC2×C5×C16C23
hypercenterC23×C16D5
hypocenterC5C2×C22⋊C32
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C16 ◁ C23×C16

342 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, 89759);