Finite Group Databasebeta

C2×#13129735 #16780136

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13129735

Splittings

FittingC22×C13×C22⋊C4 ⋊ C4
SylowC13 ⋊ C2×#1304

Subgroups

subgroupG/H
centerC23(C2×#261)⋊C4
commutatorC23×C13C2×C42
FrattiniC24C22×#261
FittingC22×C13×C22⋊C4C4
socleC23×C13#95
prime radicalC25×D13C22
cosocleC24×D13C23
hypercenterC22×C22⋊C4#261
hypocenterC13C2×#1304
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

2414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 1086785);