Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#16864385 |
| Fitting | C4×C8×C269 ⋊ C2 |
| Sylow | C269 ⋊ C4×M16 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
4328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#16864385, #46809164, #46809171, … |
| maximal normal subgroup of | C8×#16864385, #46809164, #46809171, … |
| maximal quotient of | C8×#16864385, #46809171, #46809179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 499);