Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C7 ⋊ #487 |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,10,11,15)(9,13,12,14)(17,20)(18,23)(21,22);(8,9,11,12)(10,14,15,13);(2,3)(4,5)(6,7)(9,12)(13,14)(16,17,19,22)(18,20,23,21)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=ce,d^c=df64 conjugacy classes — view the full character table.
| maximal subgroup of | #11726188, #11726189, #11726199, … |
| maximal normal subgroup of | #11726188, #11726189, #11726199, … |
| maximal quotient of | #11727328, #11727333, #11727343, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 627);