Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#117 ⋊ 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)(9,14,15,16)(10,17)(13,20,21,22)(18,23);(8,10)(9,13)(11,18)(12,17)(14,22)(15,21)(16,20)(19,23);(2,3)(4,5)(6,7)(8,9)(10,13)(11,14)(12,15)(16,19)(17,21)(18,22)(20,23)Polycyclic presentation:
2^6,7|c^2=d,e^2=f,c^a=ce,d^a=df,e^a=ef,g^a=g^6,c^b=cf82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726454, #11726457, #11726458, … |
| maximal normal subgroup of | #11726454, #11726457, #11726458, … |
| maximal quotient of | #11727184, #11727194, #11727195, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 539);