Finite Group Databasebeta

C22×#16861148 #30651825

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

Aliases

direct productC22×#16861148

Splittings

FittingC22×C16×C127 ⋊ C2
SylowC127 ⋊ C22×M32

Subgroups

subgroupG/H
centerC22×C8C2×D127
commutatorC2×C127C23×C8
FrattiniC8C23×D127
FittingC22×C16×C127C2
socleC23×C127C2×C8
prime radicalC23×D127C8
cosocleC8×C127C24
hypercenterC22×C16D127
hypocenterC127C22×M32
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C22×C8 ◁ C22×C16

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, 17605);