Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×#11761640 |
| unambiguous semidirect product | D269⋊(C2×C42) |
| Fitting | C22×C4×C269 ⋊ C4 |
| derived, Sylow | C269 ⋊ C22×C42 |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
1136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #95×#11761640, C4×(C2×#11761640)⋊C4, #46826060, … |
| maximal normal subgroup of | #95×#11761640, C4×(C2×#11761640)⋊C4, #46826060, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1609);