Finite Group Databasebeta

C2×#22551666 #30657792

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

Aliases

direct productC2×#22551666

Splittings

SylowC257 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C4C2×#11759967
commutatorC2×C257C22×C8
FrattiniC4C22×#11759967
FittingC22×C4×C257C4
socleC22×C257C2×C8
prime radicalC23×C257C8
cosocle#14523339C23
hypercenterC22×C4#11759967
hypocenterC257C2×M32
LCSG ▷ C2×C257 ▷ C257
UCSC1 ◁ C2×C4 ◁ C22×C4

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8224

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16448, 1604);