Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#6442 |
| Sylow | C7 ⋊ C2×#126 |
246 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 246 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) = 25 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(3,4,6,8,9,7,5)(10,12)(11,14)(13,17)(15,16)(18,20)(19,22)(21,24)(23,25);(12,17)(14,16)(18,20,21,24)(19,22,23,25);(4,5)(6,7)(8,9)(10,11,13,15)(12,16,17,14)(18,19,21,23)(20,22,24,25);(1,2)88 conjugacy classes — view the full character table.
| maximal subgroup of | #11725859, C4×#6442, #11730895, … |
| maximal normal subgroup of | #11725859, C4×#6442, #11730895, … |
| maximal quotient of | C2×#89423, C2×#89424, C2×#89425, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 935);