Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×Dic269 |
| Sylow | C269 ⋊ C4×M16 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46810676, #100×Dic269, #46810680, … |
| maximal normal subgroup of | #46810676, #100×Dic269, #46810680, … |
| maximal quotient of | M16×#14524130, #46809166, #46809172, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 500);