Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#22579878 |
| Sylow | C277 ⋊ C2×C4⋊Q8 |
290 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
2788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47983557, #47983558, #47983560, … |
| maximal normal subgroup of | #47983557, #47983558, #47983560, … |
| maximal quotient of | C2×#31799871, C2×#31799897, C2×#31799907, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1091);