Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#22579868 |
| Fitting | C2×C42×C277 ⋊ C2 |
| Sylow | C277 ⋊ C2×#124 |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
4444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981518, #47981520, C2×#31799741, … |
| maximal normal subgroup of | #47981518, #47981520, C2×#31799741, … |
| maximal quotient of | C2×#31799868, C2×#31799893, C2×#31799904, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1066);