Finite Group Databasebeta

C2×#22550688 #30653491

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

Aliases

direct productC2×#22550688

Splittings

FittingC2×#131×C127 ⋊ C2
SylowC127 ⋊ C2×#577

Subgroups

subgroupG/H
centerC22C22×D508
commutator, cosocleC4×C127C25
FrattiniC4C24×D127
FittingC2×#131×C127C2
socleC22×C127C22×D4
hypercenterC2×#131D127
hypocenterC127C2×#577
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

1460 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 19271);