Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#6509 |
| Fitting | C22×C7×Q8 ⋊ C2 |
| Sylow | C7 ⋊ C2×C22⋊Q8 |
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 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)(14,16,17,21)(15,18,19,20);(1,2)(14,15,17,19)(16,20,21,18);(4,6)(8,9)(10,11)(12,13);(1,2)88 conjugacy classes — view the full character table.
| maximal subgroup of | #11727869, #11727997, #11727998, … |
| maximal normal subgroup of | #11727869, #11727997, #11727998, … |
| maximal quotient of | C2×#89750, C2×#89745, C2×#89756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1266);