Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #430 |
102 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)(8,10,12,20,13,18,11,19)(9,14,15,17,16,22,21,23);(10,18)(14,22)(17,23)(19,20);(2,3)(4,5)(6,7)(8,9,11,15,13,16,12,21)(10,17,19,22,18,23,20,14)Polycyclic presentation:
2^6,7|a^2=d,c^2=e,d^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^6,c^b=cf82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726455, #11726469, #11726472, … |
| maximal normal subgroup of | #11726455, #11726469, #11726472, … |
| maximal quotient of | #11727594, #11727595, #11727596, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 659);