Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#6448 |
| Fitting | C2×C7×C22⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ C2×#124 |
330 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(4,6)(7,8,10,12,13,11,9)(14,16)(15,19)(17,21)(18,20);(3,4,5,6)(15,18)(16,21);(4,6)(8,9)(10,11)(12,13)(14,15)(16,20)(17,18)(19,21);(1,2)88 conjugacy classes — view the full character table.
| maximal subgroup of | #11725858, C4×#6448, #11730897, … |
| maximal normal subgroup of | #11725858, C4×#6448, #11730897, … |
| maximal quotient of | C2×#89422, C2×#89441, C2×#89442, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 944);