Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C7 ⋊ #491 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,4,6,7,5,3)(8,10,11,15)(9,13,12,14)(17,22)(18,25)(19,27)(21,28)(23,24)(29,30);(8,9,11,12)(10,14,15,13)(16,18)(17,21)(19,26)(20,25)(22,30)(23,28)(24,29)(27,31);(2,3)(4,5)(6,7)(9,12)(13,14)(16,17,20,24)(18,21,25,29)(19,22,27,23)(26,30,31,28)Polycyclic presentation:
2^6,7|a^2=f,b^2=e,c^2=e,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^6,c^b=cef,d^c=df58 conjugacy classes — view the full character table.
| maximal subgroup of | #11726128, #11726131, #11726133, … |
| maximal normal subgroup of | #11726128, #11726131, #11726133, … |
| maximal quotient of | #11727302, #11727306, #11727314, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 603);