Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C13×#585 ⋊ C4 |
| Sylow | C13 ⋊ #62654 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C25×#261 |
| commutator, socle | C2×C13 | C25×C4 |
| Fitting | C13×#585 | C4 |
| prime radical | D13×#585 | C2 |
| cosocle | C2×D13 | C26 |
| hypercenter | #585 | #261 |
| hypocenter | C13 | #62654 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ #585 | |
11222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^8,13|a^2=h,f^2=g,b^a=bg,f^a=fg,i^a=i^8,e^b=eg,d^c=dg,i^h=i^12232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1116289);