Finite Group Databasebeta

C2×#13131373 #16807610

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13131373
unambiguous semidirect productD13⋊#2373

Splittings

FittingC2×C13×#126 ⋊ C4
SylowC13 ⋊ C2×#2373

Subgroups

subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×#126C4
socleC23×C13C23×C4
prime radicalC24×D13C23
cosocleC22×D13C25
hypercenterC2×#126#261
hypocenterC13C2×#2373
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#126

2726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114259);