Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| 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)(9,15)(10,19)(11,22)(12,23)(14,26)(16,17)(18,32)(20,36)(24,33)(25,31)(27,38)(28,39)(29,30)(34,37);(8,10)(9,14)(11,20)(12,21)(13,19)(15,30)(16,27)(17,28)(18,29)(22,37)(23,35)(24,34)(25,38)(26,32)(31,39)(33,36);(2,3)(4,5)(6,7)(8,9,13,18)(10,14,19,29)(11,15,24,32)(12,25,23,17)(16,33,31,22)(20,30,34,26)(21,38,35,28)(27,36,39,37)Polycyclic presentation:
2^6,7|a^2=f,d^2=ef,e^2=f,c^a=cd,d^a=de,e^a=ef,g^a=g^6,c^b=cf,d^c=de,e^c=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | #11726998, #11726999, #11727002, … |
| maximal normal subgroup of | #11726998, #11726999, #11727002, … |
| maximal quotient of | #11728403, #11728408, #11728409, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 729);