Finite Group Databasebeta

#16791434

order3328
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #13639

Subgroups

subgroupG/H
centerC4×C8C2×#261
commutatorC2×C13C22×C32
FrattiniC2×C8C22×#261
FittingC2×C4×C8×C13C4
socleC22×C13C22×C16
prime radicalC23×C13C2×C16
cosocleC2×#6090C23
hypercenterC2×C4×C8#261
hypocenterC13#13639
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C4×C8 ◁ C2×C4×C8

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Polycyclic presentation:

2^8,13|a^2=e,c^2=d,e^2=f,f^2=g,g^2=h,b^a=bd,i^a=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, 1098083);