Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D7×C4⋊C4 |
| Fitting | C2×C7×C4⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ C22×C4⋊C4 |
418 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 418 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) = 224 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5,6)(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×#324, #11725898, D7×#340, … |
| maximal normal subgroup of | D7×#324, #11725898, D7×#340, … |
| maximal quotient of | C2×#89421, C2×#89422, C2×#89419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 954);