Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#131 ⋊ C2 |
| Sylow | C7 ⋊ #471 |
104 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 104 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)(8,10)(9,14)(11,17)(12,18)(13,20)(15,23)(16,19)(21,22);(8,9,11,13,12,15,19,21)(10,14,17,20,18,23,16,22);(2,3)(4,5)(6,7)(9,13)(10,16)(11,19)(15,21)(17,18)(20,22)Polycyclic presentation:
2^6,7|b^2=e,d^2=f,e^2=f,b^a=be,c^a=cd,d^a=df,e^a=ef,g^a=g^6,d^c=df76 conjugacy classes — view the full character table.
| maximal subgroup of | #11737337, #11737338, #11737345, … |
| maximal normal subgroup of | #11737337, #11737338, #11737345, … |
| maximal quotient of | #11727645, #11727646, #11727647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 675);