Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #89246 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #332 |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(9,12)(10,15)(13,14)(16,17,18,22,20,23,19,21);(2,3)(4,5)(6,7)(8,9,11,14)(10,12,15,13)(17,21)(18,19)(22,23)Polycyclic presentation:
2^6,7|a^2=e,b^2=c,c^2=ef,d^2=f,b^a=bd,c^a=cef,d^a=df,g^a=g^6,d^b=de79 conjugacy classes — view the full character table.
| maximal subgroup of | #11725939, #11725947, #11725954, … |
| maximal normal subgroup of | #11725939, #11725947, #11725954, … |
| maximal quotient of | #11725283, #11725369, #11725370, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 43);