Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #471 |
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 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)(8,9,12,16)(10,17,20,22)(11,14,21,15)(13,18,23,19)Polycyclic presentation:
2^6,7|a^2=f,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, #11737726, #11737733, … |
| maximal normal subgroup of | #11737725, #11737726, #11737733, … |
| maximal quotient of | #11728053, #11728056, #11728058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 734);