Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #423 |
126 conjugacy classes of subgroups.
| 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)(13,16)(17,19);(8,9,10,11);(2,3)(4,5)(6,7)(9,11)(12,13,14,17,15,16,18,19)Polycyclic presentation:
2^6,7|a^2=d,b^2=e,d^2=f,b^a=be,c^a=cf,g^a=g^6124 conjugacy classes — view the full character table.
| maximal subgroup of | #11725426, #11725437, #11725475, … |
| maximal normal subgroup of | #11725426, #11725437, #11725475, … |
| maximal quotient of | #11727145, #11727146, #11727148, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 458);