Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#106 ⋊ C2 |
| Sylow | C7 ⋊ #465 |
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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)(8,9,10,11)(13,16)(14,18)(17,19);(12,13,14,16,15,17,18,19);(2,3)(4,5)(6,7)(9,11)Polycyclic presentation:
2^6,7|b^2=e,c^2=d,e^2=f,c^a=cd,g^a=g^6,c^b=cef,e^c=ef64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89636, #11736565, #11736569, … |
| maximal normal subgroup of | C2×#89636, #11736565, #11736569, … |
| maximal quotient of | #11726290, #11726291, #11726292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 398);