Finite Group Databasebeta

C2×#22550712 #30653538

order16256
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC2×#22550712

Splittings

FittingC22×#41×C127 ⋊ C2
SylowC127 ⋊ C2×#585

Subgroups

subgroupG/H
centerC2×C4C23×D127
commutator, cosocleC2×C127C26
FrattiniC2C25×D127
FittingC22×#41×C127C2
socleC22×C127C25
hypercenterC22×#41D127
hypocenterC127C2×#585
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C22×#41

5956 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2588 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 19318);