Finite Group Databasebeta

#15784352

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #13802

Subgroups

subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#13802
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

2182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Polycyclic presentation:

2^8,13|a^2=g,b^2=h,c^2=ef,b^a=be,c^a=cf,i^a=i^12,d^b=de

Conjugacy classes & character table

580 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 91001);