Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #1132 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#1132 |
| Fitting | C4×C7×C8 ⋊ C2 |
| Sylow | C7 ⋊ C4×SD16 |
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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)(12,13,14,16,15,17,18,19);(2,3)(4,5)(6,7)(13,16)(14,18)(17,19);(8,9,10,11)124 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#1132, #11725809, #11725830, … |
| maximal normal subgroup of | C8×#1132, #11725809, #11725830, … |
| maximal quotient of | C8×#1132, #11725809, #11725833, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 225);