Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×M32 ⋊ C2 |
| Sylow | C7 ⋊ #510 |
82 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,4,6,7,5,3)(8,11,20,35,21,23,12,24,13,25,32,38,10,19,27,39)(9,15,30,36,14,28,16,22,18,31,26,34,17,29,33,37);(8,10,13,21)(9,14,18,17)(11,23,25,19)(12,20,27,32)(15,29,31,28)(16,26,33,30)(22,36,37,34)(24,38,39,35);(2,3)(4,5)(6,7)(8,9)(10,14)(11,22)(12,26)(13,18)(15,24)(16,32)(17,21)(19,34)(20,33)(23,36)(25,37)(27,30)(28,35)(29,38)(31,39)Polycyclic presentation:
2^6,7|b^2=f,c^2=de,d^2=e,e^2=f,c^a=cd,d^a=def,e^a=ef,g^a=g^6,c^b=cf76 conjugacy classes — view the full character table.
| maximal subgroup of | #11726844, #11726875, #11726882, … |
| maximal normal subgroup of | #11726844, #11726875, #11726882, … |
| maximal quotient of | #11726823, #11726831, #11726833, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 443);