Finite Group Databasebeta

C2×#13131361 #16807595

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13131361
unambiguous semidirect productD13⋊#2361

Splittings

FittingC2×C13×#121 ⋊ C4
SylowC13 ⋊ C2×#2361

Subgroups

subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×#121C4
socleC23×C13C23×C4
prime radicalC2×D13×#121C2
cosocleC22×D13C25
hypercenterC2×#121#261
hypocenterC13C2×#2361
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#121

4782 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, 1114244);