Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×Dic538 |
| Sylow | C269 ⋊ C23×Q8 |
850 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
4328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46809155, #46810808, #46810819, … |
| maximal normal subgroup of | #46809155, #46810808, #46810819, … |
| maximal quotient of | C23×#16864381, C23×C4⋊Dic269, C22×C4×Dic538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1373);