Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #343 |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,4,6,7,5,3)(12,13,14,17,15,16,18,19);(2,3)(4,5)(6,7)(8,9,10,11)(13,16)(14,18)Polycyclic presentation:
2^6,7|a^2=c,b^2=d,d^2=f,b^a=be,d^a=df,g^a=g^6,e^b=ef82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726489, #11726490, #11726517, … |
| maximal normal subgroup of | #11726489, #11726490, #11726517, … |
| maximal quotient of | #11725465, #11725474, #11725475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 111);