Finite Group Databasebeta

C2×#22550587 #30652265

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

Aliases

direct productC2×#22550587

Splittings

FittingC2×C4⋊Q8×C127 ⋊ C2
SylowC127 ⋊ C2×#554

Subgroups

subgroupG/H
centerC23C23×D127
commutator, cosocleC22×C127C25
FrattiniC22C24×D127
FittingC2×C4⋊Q8×C127C2
socleC23×C127C24
prime radicalC22×D508C22
hypercenterC2×C4⋊Q8D127
hypocenterC127C2×#554
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

1200 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, 18045);