Finite Group Databasebeta

#16727493

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

No aliases for this group.

Splittings

FittingC2×C13×#431 ⋊ C2
SylowC13 ⋊ #60210

Subgroups

subgroupG/H
centerC42C23×D13
commutator, socleC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C13×#431C2
prime radical#13128132C2
cosocleC2×C4×C13C25
hypercenterC2×#431D13
hypocenterC13#60210
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C42 ◁ C2×#431

1996 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Polycyclic presentation:

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

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, 1034142);