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)(9,13)(12,14)(16,18,26,30,20,25,19,27)(17,22,28,31,21,29,23,24);(8,10,11,15)(9,12,13,14)(17,21)(18,25)(23,28)(27,30);(2,3)(4,5)(6,7)(8,9,11,13)(10,14,15,12)(16,17,20,21)(18,24,25,31)(19,28,26,23)(22,30,29,27)Polycyclic presentation:
2^6,7|a^2=e,b^2=ef,c^2=de,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^6,c^b=cf76 conjugacy classes — view the full character table.
| maximal subgroup of | #11725327, #11726112, #11726113, … |
| maximal normal subgroup of | #11725327, #11726112, #11726113, … |
| maximal quotient of | #11726385, #11726392, #11726396, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 237);