Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #6400 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C7 ⋊ #368 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 2 generators on 39 points:
(1,2,4,6,7,5,3)(8,10,11,19,13,22,24,21)(9,14,15,27,17,29,31,28)(12,25,23,20,26,36,38,37)(16,32,30,18,33,34,39,35);(2,3)(4,5)(6,7)(8,9,12,16,24,31,38,39,13,17,26,33,11,15,23,30)(10,18,20,27,19,34,36,29,22,35,37,28,21,32,25,14)Polycyclic presentation:
2^6,7|a^2=d,b^2=c,c^2=f,d^2=ef,e^2=f,b^a=bd,g^a=g^6,d^b=de,e^b=ef64 conjugacy classes — view the full character table.
| maximal subgroup of | #11726992, #11726993, #11727014, … |
| maximal normal subgroup of | #11726992, #11726993, #11727014, … |
| maximal quotient of | #11725275, #11725276, #11725534, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 50);