Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #458 |
160 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)(9,14)(10,16)(12,18)(13,19)(15,21)(17,23)(20,22);(8,10)(9,13)(11,16)(12,17)(14,19)(15,20)(18,23)(21,22);(2,3)(4,5)(6,7)(8,9,12,15)(10,13,17,20)(11,14,18,21)(16,22,23,19)Polycyclic presentation:
2^6,7|a^2=f,b^a=be,c^a=cd,g^a=g^6,d^b=df,e^c=ef67 conjugacy classes — view the full character table.
| maximal subgroup of | #11728739, #11728740, #11728744, … |
| maximal normal subgroup of | #11728739, #11728740, #11728744, … |
| maximal quotient of | #11729409, #11729411, #11729597, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 777);