Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#6472 |
| Fitting | C2×C7×M16 ⋊ C2 |
| 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)(10,13,14,21,15,22,12,19)(11,17,16,20,18,25,23,24);(1,2)(10,12,15,14)(11,16,18,23)(13,21,22,19)(17,24,25,20);(4,5)(6,7)(8,9)(10,11)(12,16)(13,20)(14,23)(15,18)(17,21)(19,25)(22,24);(1,2)82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726461, #11726479, #11726516, … |
| maximal normal subgroup of | #11726461, #11726479, #11726516, … |
| maximal quotient of | C2×#89474, C2×#89482, C2×#89486, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1200);