Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #494 |
122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,4,6,7,5,3)(9,11)(12,14,16,22)(13,17,19,26)(15,24,25,21)(18,27,23,20);(9,11)(12,13,16,19)(14,20,22,27)(15,23,25,18)(17,24,26,21);(2,3)(4,5)(6,7)(8,9,10,11)Polycyclic presentation:
2^6,7|a^2=e,b^2=f,c^2=f,d^2=f,b^a=be,c^a=ce,g^a=g^6,c^b=cd,d^b=df,d^c=df64 conjugacy classes — view the full character table.
| maximal subgroup of | #11726969, #11726972, #11726988, … |
| maximal normal subgroup of | #11726969, #11726972, #11726988, … |
| maximal quotient of | #11727979, #11728003, #11728012, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 715);