Finite Group Databasebeta

#16786646

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C4

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #11409

Subgroups

subgroupG/H
center, FrattiniC2×C8C22×#261
commutator, socleC22×C13C2×C4×C8
FittingC2×C13×M32C4
prime radicalC23×C13C4×C8
cosocleC8×Dic13C23
hypercenterC2×M32#261
hypocenterC13#11409
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C2×M32

284 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,g^2=h,c^a=cf,i^a=i^8,c^b=ch,i^d=i^12

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1093295);