Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #443 |
106 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,11)(9,15)(10,16)(12,20)(13,14)(17,18)(19,23)(21,22);(8,10)(9,14)(11,17)(12,18)(13,19)(15,22)(16,21)(20,23);(2,3)(4,5)(6,7)(8,9,12,16,13,17,22,23)(10,14,18,21,19,11,15,20)Polycyclic presentation:
2^6,7|a^2=d,d^2=f,e^2=f,g^a=g^6,c^b=ce,e^b=ef,e^c=ef70 conjugacy classes — view the full character table.
| maximal subgroup of | #11726992, #11726993, #11727000, … |
| maximal normal subgroup of | #11726992, #11726993, #11727000, … |
| maximal quotient of | #11728041, #11728043, #11728045, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 730);