Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C7×SD16 ⋊ C2 |
| Sylow | C7 ⋊ #492 |
142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,7,5,3)(9,11)(13,16)(14,18)(17,19);(12,13,14,16,15,17,18,19);(2,3)(4,5)(6,7)(8,9)(10,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^6,7|b^2=e,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^6,c^b=cef,e^c=ef64 conjugacy classes — view the full character table.
| maximal subgroup of | #11737082, #11737084, #11737107, … |
| maximal normal subgroup of | #11737082, #11737084, #11737107, … |
| maximal quotient of | #11727911, #11727938, #11727943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 709);