Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#6478 |
| Fitting | C2×C7×SD16 ⋊ C2 |
| Sylow | C7 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 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)(11,16)(12,18)(13,21)(15,22)(19,20)(23,25);(1,2)(10,12,14,20)(11,15,16,23)(13,18,21,19)(17,25,24,22);(4,5)(6,7)(8,9)(10,11)(12,15)(13,17)(14,16)(18,25)(19,22)(20,23)(21,24);(1,2)64 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#6478, #11737093, #11737116, … |
| maximal normal subgroup of | C4×#6478, #11737093, #11737116, … |
| maximal quotient of | C2×#89529, C2×#89531, C2×#89537, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1213);