Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C7×M16 ⋊ C2 |
| Sylow | C7 ⋊ #421 |
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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)(8,10,11,19,13,18,12,21)(9,14,15,23,16,22,20,17);(10,18)(14,22)(17,23)(19,21);(2,3)(4,5)(6,7)(8,9)(10,17)(11,15)(12,20)(13,16)(14,19)(18,23)(21,22)Polycyclic presentation:
2^6,7|c^2=d,d^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^6,c^b=cf,e^c=ef82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726459, #11726462, #11726479, … |
| maximal normal subgroup of | #11726459, #11726462, #11726479, … |
| maximal quotient of | #11727552, #11727553, #11727555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 673);