Finite Group Databasebeta

C2×#13131323 #16807525

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

Aliases

direct productC2×#13131323
unambiguous semidirect productD13⋊#2323

Splittings

FittingC2×C13×C22⋊Q8 ⋊ C4
SylowC13 ⋊ C2×#2323

Subgroups

subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×C22⋊Q8C4
socleC23×C13C23×C4
prime radicalC24×D13C23
cosocleC22×D13C25
hypercenterC2×C22⋊Q8#261
hypocenterC13C2×#2323
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

3198 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, 1114174);