Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×(C2×D7)⋊C4 |
| Fitting | C2×C42×C7 ⋊ C2 |
| Sylow | C7 ⋊ C4×C22⋊C4 |
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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) = 224 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,7,5,3)(12,13,14,15)(17,19);(2,3)(4,5)(6,7)(16,17)(18,19);(8,9,10,11)136 conjugacy classes — view the full character table.
| maximal subgroup of | #11726369, #11726370, #11726401, … |
| maximal normal subgroup of | #11726369, #11726370, #11726401, … |
| maximal quotient of | C4×#6379, #11727156, #11727159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 472);