Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#108 ⋊ C2 |
| Sylow | C7 ⋊ #443 |
106 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,11,12,21,13,19,22,14)(9,15,16,23,18,10,17,20);(8,10,12,20,13,15,22,23)(9,14,17,19,18,21,16,11);(2,3)(4,5)(6,7)(8,9)(10,19)(11,15)(12,16)(13,18)(14,20)(17,22)(21,23)Polycyclic presentation:
2^6,7|b^2=e,c^2=d,d^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^6,c^b=cef,e^c=ef70 conjugacy classes — view the full character table.
| maximal subgroup of | #11726992, #11726993, #11727016, … |
| maximal normal subgroup of | #11726992, #11726993, #11727016, … |
| maximal quotient of | #11726270, #11726275, #11726276, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 429);