Finite Group Databasebeta

C22×#16861149 #30651826

order16256
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC22×#16861149

Splittings

SylowC127 ⋊ C22×M32

Subgroups

subgroupG/H
centerC22×C8C2×D127
commutatorC2×C127C23×C8
FrattiniC8C23×D127
FittingC23×C8×C127C2
socleC23×C127C2×C8
prime radicalC24×C127C8
cosocleC8×C127C24
hypercenterC23×C8D127
hypocenterC127C22×M32
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C22×C8 ◁ C23×C8

400 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, 17606);