Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #432 |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(10,14)(12,15)(16,17,18,21,19,20,22,23);(8,10)(9,12)(11,14)(13,15);(2,3)(4,5)(6,7)(8,9,11,13)(10,12,14,15)(17,20)(21,23)Polycyclic presentation:
2^6,7|a^2=e,c^2=d,d^2=f,c^a=cf,g^a=g^6,c^b=ce88 conjugacy classes — view the full character table.
| maximal subgroup of | #11725856, #11725857, #11725858, … |
| maximal normal subgroup of | #11725856, #11725857, #11725858, … |
| maximal quotient of | #11726351, #11726357, #11726359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 253);