Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#6380 |
| Fitting | C2×C7×C22⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ C2×#99 |
210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 17 points:
(3,4,6,8,9,7,5)(11,14,15,17)(12,16);(4,5)(6,7)(8,9)(10,11)(12,14)(13,15)(16,17);(1,2)82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726706, #11726708, #11726711, … |
| maximal normal subgroup of | #11726706, #11726708, #11726711, … |
| maximal quotient of | C2×#89246, #11727152, C2×#89247, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 488);