Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #428 |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,7,5,3)(8,9,10,11)(13,17)(14,19)(16,18);(13,16)(17,18);(2,3)(4,5)(6,7)(12,13,14,18,15,16,19,17)Polycyclic presentation:
2^6,7|a^2=e,c^2=d,e^2=f,b^a=bf,c^a=ce,g^a=g^6,e^c=ef82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726734, #11726735, #11726736, … |
| maximal normal subgroup of | #11726734, #11726735, #11726736, … |
| maximal quotient of | #11727222, #11727235, #11727260, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 498);