Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #89332 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #333 |
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)(10,14)(16,17,19,21)(18,23,22,20);(2,3)(4,5)(6,7)(8,9,10,13,11,12,14,15)(17,20)(18,22)(21,23)Polycyclic presentation:
2^6,7|a^2=c,b^2=f,c^2=e,d^2=f,b^a=bd,d^a=def,g^a=g^6,c^b=ce,d^b=df61 conjugacy classes — view the full character table.
| maximal subgroup of | #11725356, #11725579, D7×#333, … |
| maximal normal subgroup of | #11725356, #11725579, D7×#333, … |
| maximal quotient of | #11725440, #11725448, #11725606, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 103);