Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#16864381 |
| Sylow | C269 ⋊ C4×C4⋊C4 |
194 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
4328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46810746, C8×#16864381, #46810751, … |
| maximal normal subgroup of | #46810746, C8×#16864381, #46810751, … |
| maximal quotient of | C4×#22575360, #46809111, #46809113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 402);