Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C4⋊C8×D269 |
| Fitting | C4⋊C8×C269 ⋊ C2 |
| Sylow | C269 ⋊ C2×C4⋊C8 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊C8×D269, Q8⋊C8×D269, #46809269, … |
| maximal normal subgroup of | D4⋊C8×D269, Q8⋊C8×D269, #46809269, … |
| maximal quotient of | #334×D269, #335×D269, #46809630, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 568);