Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #473 |
100 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)(9,16)(10,21)(12,28)(13,26)(14,27)(15,29)(17,33)(18,25)(19,32)(20,34)(22,38)(23,36)(24,37)(30,39)(31,35);(8,10,12,22,14,24,13,23)(9,15,17,30,19,31,18,20)(11,21,28,38,27,37,26,36)(16,29,33,39,32,35,25,34);(2,3)(4,5)(6,7)(8,9,14,19)(10,20,24,30)(11,25,27,33)(12,18,13,17)(15,22,31,23)(16,28,32,26)(21,35,37,29)(34,38,39,36)Polycyclic presentation:
2^6,7|a^2=f,b^2=ef,d^2=f,e^2=f,b^a=be,c^a=cd,d^a=df,e^a=ef,g^a=g^6,d^c=df76 conjugacy classes — view the full character table.
| maximal subgroup of | #11726882, #11726883, #11728847, … |
| maximal normal subgroup of | #11726882, #11726883, #11728847, … |
| maximal quotient of | #11727645, #11727648, #11727658, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 677);