Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#6449 |
| Fitting | C2×C7×C22⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ C2×#123 |
342 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 127 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:
(3,4,5,6)(7,8,10,12,13,11,9)(15,19)(16,21);(1,2)(14,16)(15,18)(17,21)(19,20);(4,6)(8,9)(10,11)(12,13)(14,15)(16,20)(17,19)(18,21);(1,2)88 conjugacy classes — view the full character table.
| maximal subgroup of | #11726708, #11726717, #11726720, … |
| maximal normal subgroup of | #11726708, #11726717, #11726720, … |
| maximal quotient of | C2×#89425, C2×#89442, C2×#89446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 945);