Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#123 ⋊ C2 |
| Sylow | C7 ⋊ #458 |
160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,11,12,18)(9,14,15,22)(10,16,17,23)(13,19,20,21);(8,10)(9,13)(11,16)(12,17)(14,21)(15,20)(18,23)(19,22);(2,3)(4,5)(6,7)(8,9)(10,13)(11,14)(12,15)(16,21)(17,20)(18,22)(19,23)Polycyclic presentation:
2^6,7|c^2=f,c^a=cd,e^a=ef,g^a=g^6,c^b=ce,d^b=df58 conjugacy classes — view the full character table.
| maximal subgroup of | #11726892, #11726893, #11726894, … |
| maximal normal subgroup of | #11726892, #11726893, #11726894, … |
| maximal quotient of | #11727290, #11727292, #11727293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 587);