Finite Group Databasebeta

#16726552

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #60099

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D13
commutator, socleC22×C13C24×C4
FittingC2×C4×C13×#41C2
prime radicalC22×C13×#41C22
cosocleC2×C4×C13C25
hypercenterC2×C4×#41D13
hypocenterC13#60099
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×#41

2738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Polycyclic presentation:

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

Conjugacy classes & character table

568 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033201);