Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×D7×M16 |
| Fitting | C2×C7×M16 ⋊ C2 |
| Sylow | C7 ⋊ C22×M16 |
298 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 159 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)(15,17);(10,11,12,15,13,14,16,17);(4,5)(6,7)(8,9);(1,2)100 conjugacy classes — view the full character table.
| maximal subgroup of | D7×H(3,ℤ/4), D7×#338, D7×#339, … |
| maximal normal subgroup of | D7×H(3,ℤ/4), D7×#338, D7×#339, … |
| maximal quotient of | C2×#89473, #11735927, C2×D7×#97, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1196);