Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C269 ⋊ #379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D269 |
| commutator | C22×C269 | C22×C4 |
| Fitting, prime radical | C25×C269 | C2 |
| socle, cosocle | C23×C269 | C23 |
| hypercenter | C25 | D269 |
| hypocenter | C269 | #379 |
| LCS | G ▷ C22×C269 ▷ C269 | |
| UCS | C1 ◁ C23 ◁ C25 | |
506 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|a^2=f,b^a=bd,c^a=ce,g^a=g^2684316 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46808789, #46810799, #46810800, … |
| maximal normal subgroup of | #46808789, #46810799, #46810800, … |
| maximal quotient of | #46809108, #46809126, #46809156, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 405);