Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #444 |
104 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)(9,16)(10,18)(12,22)(13,23)(14,15)(17,20)(19,21);(8,10)(9,15)(11,19)(12,16)(13,21)(14,20)(17,23)(18,22);(2,3)(4,5)(6,7)(8,9,12,17,14,19,13,18)(10,15,16,23,20,11,21,22)Polycyclic presentation:
2^6,7|a^2=d,d^2=f,e^2=f,c^a=cf,g^a=g^6,c^b=ce,e^b=ef,e^c=ef64 conjugacy classes — view the full character table.
| maximal subgroup of | #11727002, #11727003, #11729269, … |
| maximal normal subgroup of | #11727002, #11727003, #11729269, … |
| maximal quotient of | #11728042, #11728044, #11728045, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 731);