Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#22579797 |
| Sylow | C277 ⋊ C2×#100 |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4432 |
2782 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981284, #47981285, C4×#22579797, … |
| maximal normal subgroup of | #47981284, #47981285, C4×#22579797, … |
| maximal quotient of | C2×#31799726, #47981488, #47981494, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 526);