Finite Group Databasebeta

C2×#13129953 #16791176

order3328
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×#13129953

Splittings

SylowC13 ⋊ C2×#1401

Subgroups

subgroupG/H
centerC2×C8C22⋊#261
commutatorC4×C13C22×C16
FrattiniC2×C8C22×#261
FittingC2×C13×#131C4
socleC22×C13C22⋊C16
prime radicalC2×C13×#41C8
cosocleC2×#6090C23
hypercenterC2×#131#261
hypocenterC13C2×#1401
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#131

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1097825);