Finite Group Databasebeta

#16727438

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

Aliases

No aliases for this group.

Splittings

FittingC13×#2932 ⋊ C2
SylowC13 ⋊ #60205

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D13
commutator, socleC22×C13C24×C4
FittingC13×#2932C2
prime radical#13128131C2
cosocleC2×C4×C13C25
hypercenter#2932D13
hypocenterC13#60205
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #2932

1950 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^a=eh,c^b=ch,i^b=i^12,i^d=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, 1034087);