Finite Group Databasebeta

C2×#13130005 #16791497

order3328
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13130005

Splittings

SylowC13 ⋊ C2×M128

Subgroups

subgroupG/H
centerC2×C16C2×#261
commutatorC2×C13C22×C32
FrattiniC16C22×#261
FittingC22×C13×C16C4
socleC22×C13C2×C32
prime radicalC23×C13C32
cosocle#88034C23
hypercenterC22×C16#261
hypocenterC13C2×M128
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C16 ◁ C22×C16

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1098146);