Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #89261 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C7⋊#338 |
| Sylow | C7 ⋊ #338 |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(8,10,11,20,13,21,12,19)(9,14,16,18,17,22,15,23);(2,3)(4,5)(6,7)(8,9,11,15,13,17,12,16)(10,18,19,22,21,23,20,14)Polycyclic presentation:
2^6,7|a^2=c,b^2=d,c^2=f,d^2=f,e^2=f,b^a=be,d^a=df,g^a=g^6,c^b=cf82 conjugacy classes — view the full character table.
| maximal subgroup of | #11725341, #11725343, #11725585, … |
| maximal normal subgroup of | #11725341, #11725343, #11725585, … |
| maximal quotient of | #11725466, #11725476, #11725485, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 117);