Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#137 ⋊ C2 |
| Sylow | C7 ⋊ #456 |
142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 142 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)(8,11,14,15)(9,16,18,23)(10,19,20,17)(12,22,13,21);(8,10,14,20)(9,15,18,11)(12,16,13,23)(17,22,19,21);(2,3)(4,5)(6,7)(8,9)(10,15)(11,20)(12,19)(13,17)(14,18)(16,21)(22,23)Polycyclic presentation:
2^6,7|b^2=f,c^2=f,d^2=f,e^2=f,c^a=cd,d^a=df,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 | #11737736, #11737738, D7×#456, … |
| maximal normal subgroup of | #11737736, #11737738, D7×#456, … |
| maximal quotient of | #11728051, #11728062, #11728063, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 739);