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)(8,10,11,19,13,20,12,21)(9,15,16,18,14,22,17,23);(9,14)(15,22)(16,17)(18,23);(2,3)(4,5)(6,7)(8,9,12,17,13,14,11,16)(10,18,19,22,20,23,21,15)Polycyclic presentation:
2^6,7|a^2=e,c^2=d,d^2=f,e^2=f,b^a=bf,c^a=ce,g^a=g^6,e^c=ef82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726460, #11726463, #11726476, … |
| maximal normal subgroup of | #11726460, #11726463, #11726476, … |
| maximal quotient of | #11727627, #11727629, #11727737, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 658);