Finite Group Databasebeta

C2×#13129937 #16789235

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13129937

Splittings

FittingC22×C13×M16 ⋊ C4
SylowC13 ⋊ C2×#1395

Subgroups

subgroupG/H
centerC2×C4#88119
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC22×C13×M16C4
socleC22×C13#342
prime radicalC22×#6127C22
cosocleC2×#6127C23
hypercenterC22×M16#261
hypocenterC13C2×#1395
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1095884);