Finite Group Databasebeta

C2×#22549709 #30641021

order16256
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC2×#22549709

Splittings

FittingC2×C32×C127 ⋊ C2
SylowC127 ⋊ C2×M64

Subgroups

subgroupG/H
centerC2×C16C2×D127
commutatorC2×C127C22×C16
FrattiniC16C22×D127
FittingC2×C32×C127C2
socleC22×C127C2×C16
prime radicalC22×D127C16
cosocleC16×C127C23
hypercenterC2×C32D127
hypocenterC127C2×M64
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C16 ◁ C2×C32

112 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, 6801);