Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#6470 |
| Fitting | C2×C7×M16 ⋊ C2 |
| Sylow | C7 ⋊ C2×#131 |
266 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 151 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)(10,12,13,19,14,18,20,24)(11,16,17,23,15,21,22,25);(1,2)(11,15)(12,18)(17,22)(19,24);(4,5)(6,7)(8,9)(10,11)(12,16)(13,17)(14,15)(18,21)(19,23)(20,22)(24,25);(1,2)100 conjugacy classes — view the full character table.
| maximal subgroup of | #11726464, #11726478, #11726493, … |
| maximal normal subgroup of | #11726464, #11726478, #11726493, … |
| maximal quotient of | C2×#89473, #11735926, C2×#89480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1197);