Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C23×#14524130 |
| derived, Sylow | C269 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D269 |
| commutator, hypocenter | C269 | C23×C8 |
| Frattini | C4 | C23×D269 |
| Fitting | C23×C4×C269 | C2 |
| socle, prime radical | C24×C269 | C4 |
| cosocle | C4×C269 | C24 |
| LCS | G ▷ C269 | |
| UCS | C1 ◁ C23×C4 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
4352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1306);