Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D7×#100 |
| Fitting | C7×#100 ⋊ C2 |
| Sylow | C7 ⋊ C2×#100 |
186 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 56 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,4,6,7,5,3)(9,12)(10,14);(8,9,10,13,11,12,14,15);(2,3)(4,5)(6,7)55 conjugacy classes — view the full character table.
| maximal subgroup of | D7×AΣL(1,𝔽16), #11726889, D7×#352, … |
| maximal normal subgroup of | D7×AΣL(1,𝔽16), #11726889, D7×#352, … |
| maximal quotient of | #11725855, #11725857, #11725858, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 278);