Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C7×#106 ⋊ C2 |
| Sylow | C7 ⋊ #482 |
106 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 37 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) = 224 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(9,13)(12,15)(16,18,20,17,19,22,23,21);(8,10,11,14)(9,12,13,15)(16,17,19,21)(18,23,22,20);(2,3)(4,5)(6,7)(8,9)(10,12)(11,13)(14,15)(17,21)(18,22)Polycyclic presentation:
2^6,7|b^2=d,c^2=e,e^2=f,b^a=bf,c^a=cd,g^a=g^6,c^b=ce,e^b=ef61 conjugacy classes — view the full character table.
| maximal subgroup of | #11736557, C2×#89638, #11736570, … |
| maximal normal subgroup of | #11736557, C2×#89638, #11736570, … |
| maximal quotient of | #11726545, #11726575, #11726576, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 400);