Finite Group Databasebeta

C2×#13131563 #16808274

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13131563

Splittings

SylowC13 ⋊ C2×#2932

Subgroups

subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×C4⋊Q8C4
socleC23×C13C23×C4
prime radicalC2×#11719430C2
cosocleC2×Dic13C25
hypercenterC2×C4⋊Q8#261
hypocenterC13C2×#2932
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

2806 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, 1114923);