Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #418 |
190 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,7,5,3)(13,18)(14,15)(17,19);(12,14,16,15)(13,17,19,18);(2,3)(4,5)(6,7)(8,9,10,11)(12,13)(14,17)(15,18)(16,19)Polycyclic presentation:
2^6,7|a^2=d,b^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^6,c^b=cf,e^c=ef82 conjugacy classes — view the full character table.
| maximal subgroup of | #11727397, #11727417, #11727826, … |
| maximal normal subgroup of | #11727397, #11727417, #11727826, … |
| maximal quotient of | #11729308, #11729312, #11729351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 749);