Finite Group Databasebeta

#16786582

order3328
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C2×C8

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #11399

Subgroups

subgroupG/H
centerC2×C16C2×#261
commutatorC2×C13C2×C82
FrattiniC2×C8C22×#261
FittingC22×C13×C16C4
socleC22×C13C2×C4×C8
prime radicalC23×C13C4×C8
cosocleC8×Dic13C23
hypercenterC22×C16#261
hypocenterC13#11399
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C16 ◁ C22×C16

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Polycyclic presentation:

2^8,13|a^2=d,b^2=e,d^2=f,e^2=g,f^2=h,c^b=ch,i^b=i^8,i^e=i^12

Conjugacy classes & character table

352 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1093231);