Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | D7×C22⋊C8 |
| Fitting | C7×C22⋊C8 ⋊ C2 |
| Sylow | C7 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,4)(13,14,16,18,19,17,15);(1,2)(3,4)(5,6,7,9,8,10,11,12);(14,15)(16,17)(18,19)100 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#323, #11725873, #11725876, … |
| maximal normal subgroup of | D7×#323, #11725873, #11725876, … |
| maximal quotient of | #11725854, #11725855, D7×#323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 258);