Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C7×C8 ⋊ C2 |
| Sylow | C7 ⋊ #466 |
134 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)(9,11);(12,13,17,19,15,18,14,16);(2,3)(4,5)(6,7)(8,9)(10,11)(13,16)(14,17)(18,19)Polycyclic presentation:
2^6,7|b^2=ef,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^6118 conjugacy classes — view the full character table.
| maximal subgroup of | #11725291, #11725293, #11725332, … |
| maximal normal subgroup of | #11725291, #11725293, #11725332, … |
| maximal quotient of | #11727522, #11727524, #11727530, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 649);