Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C7 ⋊ #472 |
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 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) = 112 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(9,14)(10,18)(11,21)(15,16)(17,22)(19,20);(8,10)(9,13)(11,18)(12,20)(14,17)(15,22)(16,23)(19,21);(2,3)(4,5)(6,7)(8,9)(10,17)(11,14)(12,16)(13,19)(15,21)(18,23)(20,22)Polycyclic presentation:
2^6,7|d^2=f,e^2=f,b^a=be,c^a=cd,d^a=df,e^a=ef,g^a=g^6,c^b=ce,e^b=ef,d^c=df,e^c=ef49 conjugacy classes — view the full character table.
| maximal subgroup of | #11737725, #11737727, #11737732, … |
| maximal normal subgroup of | #11737725, #11737727, #11737732, … |
| maximal quotient of | #11728054, #11728055, #11728057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 733);