Finite Group Databasebeta

#15754253

order3328
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #8300

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC23×C13C22×C8
FrattiniC23×C4C22×D13
FittingC22×C13×#117C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C2×C4
cosocleC23×C4×C13C23
hypercenterC22×#117D13
hypocenterC13#8300
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#117

1158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Polycyclic presentation:

2^8,13|a^2=f,c^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^12,f^b=fg

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 60902);