Finite Group Databasebeta

C2×#22550686 #30653489

order16256
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#22550686

Splittings

FittingC2×AGL(1,ℤ/8)×C127 ⋊ C2
SylowC127 ⋊ C2×#577

Subgroups

subgroupG/H
centerC22C2×D4×D127
commutator, cosocleC4×C127C25
FrattiniC4C24×D127
FittingC2×AGL(1,ℤ/8)×C127C2
socleC22×C127C22×D4
hypercenterC2×AGL(1,ℤ/8)D127
hypocenterC127C2×#577
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

1460 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 19269);