Finite Group Databasebeta

C2×#22549711 #30641027

order16256
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×#22549711

Splittings

FittingC2×D16×C127 ⋊ C2
SylowC127 ⋊ C2×D32

Subgroups

subgroupG/H
centerC22#16861150
commutator, cosocleC16×C127C23
FrattiniC16C22×D127
FittingC2×D16×C127C2
socleC22×C127D16
hypercenterC2×D16D127
hypocenterC127C2×D32
LCSG ▷ C16×C127 ▷ C8×C127 ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×D16

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1424 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 6807);