Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #344 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(8,10,11,18,12,17,19,23)(9,13,14,20,15,16,21,22);(2,3)(4,5)(6,7)(8,9)(10,16,17,13)(11,14)(12,15)(18,22,23,20)(19,21)Polycyclic presentation:
2^6,7|a^2=c,b^2=d,d^2=f,b^a=be,e^a=ef,g^a=g^6,c^b=cf82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726458, #11726461, #11726479, … |
| maximal normal subgroup of | #11726458, #11726461, #11726479, … |
| maximal quotient of | #11725467, #11725472, #11725476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 113);