Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#6464 |
| Fitting | C22×C7×C8 ⋊ 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)(10,12,13,18,14,19,20,24)(11,16,17,23,15,21,22,25);(1,2)(11,15)(16,21)(17,22)(23,25);(4,5)(6,7)(8,9)(10,11)(12,16)(13,17)(14,15)(18,23)(19,21)(20,22)(24,25);(1,2)136 conjugacy classes — view the full character table.
| maximal subgroup of | #11726448, #11726449, #11726702, … |
| maximal normal subgroup of | #11726448, #11726449, #11726702, … |
| maximal quotient of | C2×C8×Dic14, C2×#89451, #11735890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1191);