Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#6495 |
| Fitting | C22×C7×D4 ⋊ C2 |
| Sylow | C7 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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:
(3,4,6,8,9,7,5)(11,14)(12,17)(15,16);(1,2)(10,12,13,17)(11,14,16,15);(4,5)(6,7)(8,9)(10,11)(12,14)(13,16)(15,17);(1,2)82 conjugacy classes — view the full character table.
| maximal subgroup of | #11727417, #11727418, #11727830, … |
| maximal normal subgroup of | #11727417, #11727418, #11727830, … |
| maximal quotient of | C2×#89736, C2×#89738, C2×#89740, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1246);