Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C7×#117 ⋊ C2 |
| Sylow | C7 ⋊ #410 |
158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 158 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)(8,11)(9,14,15,18)(10,16)(12,19)(13,20,21,22)(17,23);(8,10,12,17)(9,13,15,21)(11,16,19,23)(14,20,18,22);(2,3)(4,5)(6,7)(8,9)(10,13)(11,18)(12,15)(14,19)(16,22)(17,21)(20,23)Polycyclic presentation:
2^6,7|b^2=f,c^2=d,c^a=ce,d^a=df,g^a=g^6,e^c=ef82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726452, #11726458, #11726461, … |
| maximal normal subgroup of | #11726452, #11726458, #11726461, … |
| maximal quotient of | #11727185, #11727186, #11727187, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 540);