Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#6456 |
| Fitting | C2×C7×C4⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 175 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) = 224 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2)(3,4,5,6)(8,10)(11,12,14,16,17,15,13);(1,2)(7,8,9,10);(8,10)(12,13)(14,15)(16,17);(1,2)100 conjugacy classes — view the full character table.
| maximal subgroup of | #11725897, #11725899, #11726534, … |
| maximal normal subgroup of | #11725897, #11725899, #11726534, … |
| maximal quotient of | C2×#89438, C2×#89426, C2×#89441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 956);