Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×D7×C22⋊C4 |
| Fitting | C2×C7×C22⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ C22×C22⋊C4 |
674 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 207 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 — 4 generators on 17 points:
(3,4)(5,6)(7,8)(9,10)(11,12,14,16,17,15,13);(4,6)(7,8,9,10);(1,2)(12,13)(14,15)(16,17);(1,2)100 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#323, #11725874, D7×#342, … |
| maximal normal subgroup of | D7×#323, #11725874, D7×#342, … |
| maximal quotient of | C2×#89438, C2×#89418, C2×D7×#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 937);