Finite Group Databasebeta

C2×#13131222 #16807130

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13131222

Splittings

SylowC13 ⋊ C2×#2169

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC22×C13C23×C8
FrattiniC2×C4C23×#261
FittingC2×C13×C4⋊C8C4
socleC23×C13C22×C8
prime radicalC22×D52C8
cosocleC2×#1055C24
hypercenterC2×C4⋊C8#261
hypocenterC13C2×#2169
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

742 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, 1113779);