Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C13 ⋊ #34902 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D13 |
| commutator, socle, cosocle | C23×C13 | C25 |
| Fitting | C13×#2592 | C2 |
| prime radical | C22×D4×C13 | C23 |
| hypercenter | #2592 | D13 |
| hypocenter | C13 | #34902 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #2592 | |
1768 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^8,13|a^2=g,b^2=g,c^2=g,d^2=h,e^2=f,b^a=bf,c^a=cg,c^b=ch,d^b=dh,i^b=i^12,i^e=i^12304 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 340928);