Finite Group Databasebeta

C2×#13129741 #16780224

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#13129741

Splittings

SylowC13 ⋊ C2×#1307

Subgroups

subgroupG/H
centerC23(C2×#261)⋊C4
commutatorC23×C13C2×C42
FrattiniC22×C4C22×#261
FittingC2×C13×C22⋊C8C4
socleC23×C13#95
prime radicalC24×C13C42
cosocleC2×C4×Dic13C23
hypercenterC2×C22⋊C8#261
hypocenterC13C2×#1307
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

172 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1086873);