Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊#11761640 |
| unambiguous semidirect product | D269⋊(C2×C22⋊C4) |
| unambiguous semidirect product | (C2×#11761640)⋊C23 |
| Fitting | C24×C269 ⋊ C4 |
| Sylow | C269 ⋊ C22×C22⋊C4 |
674 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
1112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46826058, #46826059, #46826066, … |
| maximal normal subgroup of | #46826058, #46826059, #46826066, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1610);