Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#6514 |
| Sylow | C7 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 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:
(3,4,6,8,9,7,5)(10,12)(11,15)(13,22)(14,19)(16,25)(17,24)(18,21)(20,23);(1,2)(12,19)(15,24)(18,25)(20,22);(4,5)(6,7)(8,9)(10,11,14,17)(12,18,19,25)(13,21,23,16)(15,22,24,20);(1,2)82 conjugacy classes — view the full character table.
| maximal subgroup of | #11727758, #11727761, #11727762, … |
| maximal normal subgroup of | #11727758, #11727761, #11727762, … |
| maximal quotient of | C2×#89767, C2×#89776, C2×#89768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1276);