Finite Group Databasebeta

C2×#22551688 #30657855

order16448
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#22551688

Splittings

SylowC257 ⋊ C2×M32

Subgroups

subgroupG/H
centerC22C2×#14523348
commutatorC2×C257C22×C8
FrattiniC2C22×#14523348
Fitting, prime radicalC23×C257C8
socleC22×C257C2×C8
cosocle#14523346C23
hypercenterC23#14523348
hypocenterC257C2×M32
LCSG ▷ C2×C257 ▷ C257
UCSC1 ◁ C22 ◁ C23

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8224

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16448, 1667);