Finite Group Databasebeta

C2×#22550551 #30652226

order16256
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22550551

Splittings

FittingC2×#126×C127 ⋊ C2
SylowC127 ⋊ C2×#551

Subgroups

subgroupG/H
centerC23C23×D127
commutator, cosocleC22×C127C25
FrattiniC22C24×D127
FittingC2×#126×C127C2
socleC23×C127C24
prime radicalC2×#16861179C2
hypercenterC2×#126D127
hypocenterC127C2×#551
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C23 ◁ C2×#126

1328 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1814 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 18006);