Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C7×M32 ⋊ C2 |
| Sylow | C7 ⋊ #349 |
58 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)(8,9,10,14,11,15,17,21,12,13,16,19,18,20,22,23);(2,3)(4,5)(6,7)(9,13)(10,16)(15,20)(17,22)Polycyclic presentation:
2^6,7|b^2=c,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^6,d^b=df82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726842, #11726843, D7×#349, … |
| maximal normal subgroup of | #11726842, #11726843, D7×#349, … |
| maximal quotient of | #11725321, #11725324, #11725328, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 71);