Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D7×#137 |
| Fitting | C7×#137 ⋊ C2 |
| Sylow | C7 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 4 generators on 23 points:
(2,7)(6,15)(8,12)(9,16)(17,18,20,22,23,21,19);(1,3,5,11)(2,6,7,15)(4,13,14,10)(8,16,12,9);(1,2)(3,9)(4,12)(5,7)(6,10)(8,14)(11,16)(13,15);(18,19)(20,21)(22,23)55 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#455, #11737738, D7×#456, … |
| maximal normal subgroup of | D7×#455, #11737738, D7×#456, … |
| maximal quotient of | #11736312, #11736315, #11736323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1229);