Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#22575382 |
| Sylow | C269 ⋊ C2×C4⋊C8 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
4328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46808824, #46810733, C4×#22575382, … |
| maximal normal subgroup of | #46808824, #46810733, C4×#22575382, … |
| maximal quotient of | C2×#31770355, C2×#31770357, #46809631, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 569);