Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#131 ⋊ C2 |
| Sylow | C7 ⋊ #444 |
104 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,11,12,15,14,22,13,21)(9,10,16,18,17,19,20,23);(8,10)(9,15)(11,20)(12,18)(13,23)(14,19)(16,22)(17,21);(2,3)(4,5)(6,7)(8,9)(10,11)(12,16)(13,20)(14,17)(15,18)(19,22)(21,23)Polycyclic presentation:
2^6,7|c^2=d,d^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^6,c^b=cf,e^b=ef82 conjugacy classes — view the full character table.
| maximal subgroup of | #11737334, #11737335, D7×#444, … |
| maximal normal subgroup of | #11737334, #11737335, D7×#444, … |
| maximal quotient of | #11727642, #11727644, #11727653, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 679);