Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #442 |
132 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)(13,16)(14,18)(17,19);(12,14)(13,17)(15,19)(16,18);(2,3)(4,5)(6,7)(8,9,10,11)(12,13,15,16)(14,17,19,18)Polycyclic presentation:
2^6,7|a^2=d,e^2=f,c^a=cf,g^a=g^6,c^b=ce,e^b=ef,e^c=ef64 conjugacy classes — view the full character table.
| maximal subgroup of | #11727008, #11729269, #11737021, … |
| maximal normal subgroup of | #11727008, #11729269, #11737021, … |
| maximal quotient of | #11727906, #11727910, #11727924, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 686);