Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×C4⋊#11761640 |
| unambiguous semidirect product | D269⋊(C2×C4⋊C4) |
| Fitting | C22×C4×C269 ⋊ C4 |
| Sylow | C269 ⋊ C22×C4⋊C4 |
418 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
1112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46826062, #46826063, #46826065, … |
| maximal normal subgroup of | #46826062, #46826063, #46826065, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1611);