Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #477 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,11,12,10)(9,13,14,15)(17,19)(18,22)(21,23);(8,10,12,11)(9,13,14,15)(16,18)(17,21)(19,22)(20,23);(2,3)(4,5)(6,7)(8,9,12,14)(10,13,11,15)(16,17,20,19)(18,21,23,22)Polycyclic presentation:
2^6,7|a^2=e,b^2=ef,c^2=ef,d^2=f,c^a=ce,g^a=g^6,c^b=cd,d^b=df,d^c=df61 conjugacy classes — view the full character table.
| maximal subgroup of | #11736601, #11736603, #11736607, … |
| maximal normal subgroup of | #11736601, #11736603, #11736607, … |
| maximal quotient of | #11726544, #11726553, #11726562, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 409);