Finite Group Databasebeta

#16021148

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #33999

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC2×C13C23×C42
FrattiniC23C24×D13
FittingC2×C4×C13×#41C2
socle, cosocleC23×C13C25
prime radicalC22×C13×#41C22
hypercenterC2×C4×#41D13
hypocenterC13#33999
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

3598 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=g,e^2=f,b^a=bf,d^a=df,c^b=cf,i^b=i^12

Conjugacy classes & character table

616 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 327797);