Finite Group Databasebeta

C22×C127⋊#95 #30641054

order16256
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28

Aliases

direct productC22×C127⋊#95

Splittings

SylowC127 ⋊ C22×#95

Subgroups

subgroupG/H
centerC25C2×D127
commutatorC2×C127C22×C42
FrattiniC23C23×D127
FittingC24×C4×C127C2
socle, prime radicalC25×C127C22
cosocleC23×C127C24
hypercenterC24×C4D127
hypocenterC127C22×#95
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C25 ◁ C24×C4

1880 conjugacy classes of subgroups; only the 981 normal subgroups are shown.

normal subgroups only

This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 981 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

4112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 6834);