Finite Group Databasebeta

C2×#13129716 #16779840

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#13129716

Splittings

FittingC22×C13×M16 ⋊ C4
SylowC13 ⋊ C2×#1297

Subgroups

subgroupG/H
centerC22×C4C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC22×C13×M16C4
socleC23×C13#95
prime radicalC24×D13D4
cosocleC22×C4×D13C23
hypercenterC22×M16#261
hypocenterC13C2×#1297
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

1226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1086489);