Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C7×#117 ⋊ C2 |
| Sylow | C7 ⋊ #482 |
106 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 106 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) = 224 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,10,11,14)(9,13,12,15)(16,18,20,22)(17,21,19,23);(9,12)(13,15)(16,17,20,19)(18,21,22,23);(2,3)(4,5)(6,7)(8,9)(10,13)(11,12)(14,15)(17,19)(18,21)(22,23)Polycyclic presentation:
2^6,7|b^2=f,c^2=e,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^6,d^c=df79 conjugacy classes — view the full character table.
| maximal subgroup of | #11736290, #11736291, #11736296, … |
| maximal normal subgroup of | #11736290, #11736291, #11736296, … |
| maximal quotient of | #11727214, #11727215, #11727216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 537);