Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C7 ⋊ #453 |
168 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 168 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) = 15 |
| transitive degree | μt(G) = 56 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,4,6,7,5,3)(9,12)(10,15)(13,14);(8,9)(10,12)(11,13)(14,15);(2,3)(4,5)(6,7)(10,15)(12,14)Polycyclic presentation:
2^6,7|e^2=f,c^a=cd,e^a=ef,g^a=g^6,c^b=ce,d^b=df,e^b=ef,e^c=ef49 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#453, #11737723, #11737729, … |
| maximal normal subgroup of | D7×#453, #11737723, #11737729, … |
| maximal quotient of | #11728051, #11728059, #11728060, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 732);