Finite Group Databasebeta

C22×#41×D127 #30653526

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

Aliases

direct productC22×#41×D127

Splittings

FittingC22×#41×C127 ⋊ C2
SylowC127 ⋊ C23×#41

Subgroups

subgroupG/H
centerC22×C4C22×D127
commutator, cosocleC2×C127C26
FrattiniC2C25×D127
FittingC22×#41×C127C2
socleC23×C127C24
hypercenterC22×#41D127
hypocenterC127C23×#41
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C22×C4 ◁ C22×#41

6520 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 19306);