Finite Group Databasebeta

C2×#22551687 #30657854

order16448
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×#22551687

Splittings

derived, SylowC257 ⋊ C22×C16

Subgroups

subgroupG/H
center, hypercenterC2×C4#14523348
commutator, hypocenterC257C22×C16
FrattiniC2C22×#14523348
FittingC2×C4×C257C8
socleC22×C257C2×C8
prime radicalC22×D257C8
cosocle#14523346C23
LCSG ▷ C257
UCSC1 ◁ C2×C4

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8224

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16448, 1666);