Finite Group Databasebeta

C22×#16861215 #30653434

order16256
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#16861215

Splittings

FittingC23×C8×C127 ⋊ C2
SylowC127 ⋊ C22×#131

Subgroups

subgroupG/H
centerC22×C8C2×D127
commutatorC2×C127C24×C4
FrattiniC4C24×D127
FittingC23×C8×C127C2
socleC23×C127C22×C4
prime radicalC22×#14523248C2
cosocleC4×C127C25
hypercenterC23×C8D127
hypocenterC127C22×#131
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C22×C8 ◁ C23×C8

1504 conjugacy classes of subgroups.

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, 19214);