Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×D7×SD16 |
| Fitting | C2×C7×SD16 ⋊ C2 |
| Sylow | C7 ⋊ C22×SD16 |
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2)(3,4,6,8,9,7,5)(11,14)(12,17)(15,16);(1,2)(10,11,13,16)(12,14,17,15);(4,5)(6,7)(8,9);(1,2)70 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D7×SD16, #11737094, SD16×D28, … |
| maximal normal subgroup of | C4×D7×SD16, #11737094, SD16×D28, … |
| maximal quotient of | C2×#89530, C2×#89533, C2×#89532, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1211);