Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q16×D269 |
| Fitting | C2×Q16×C269 ⋊ C2 |
| Sylow | C269 ⋊ C22×Q16 |
258 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
1904 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #358×D269, #46812603, #362×D269, … |
| maximal normal subgroup of | #358×D269, #46812603, #362×D269, … |
| maximal quotient of | C2×#103×D269, C2×#107×D269, C4×Q16×D269, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1324);