Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#6477 |
| Fitting | C2×C7×SD16 ⋊ C2 |
| Sylow | C7 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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:
(1,2)(3,4,6,8,9,7,5)(10,11,13,14)(12,17,16,15);(1,2)(11,15)(12,16)(14,17);(4,5)(6,7)(8,9)(11,14)(15,17);(1,2)64 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#6477, #11737092, #11737115, … |
| maximal normal subgroup of | C4×#6477, #11737092, #11737115, … |
| maximal quotient of | C2×#89557, C2×#89538, C2×#89536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1212);