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×#99 ⋊ C2 |
| Sylow | C7 ⋊ #410 |
158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 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)(10,16,17,18)(12,19)(13,20,21,22)(15,23);(8,10)(9,13)(11,18)(12,17)(14,22)(15,21)(16,19)(20,23);(2,3)(4,5)(6,7)(8,9,12,15)(10,13,17,21)(11,14,19,23)(16,20,18,22)Polycyclic presentation:
2^6,7|a^2=f,c^2=d,g^a=g^6,c^b=ce,d^b=df,e^c=ef55 conjugacy classes — view the full character table.
| maximal subgroup of | #11726890, #11726891, #11726898, … |
| maximal normal subgroup of | #11726890, #11726891, #11726898, … |
| maximal quotient of | #11725854, #11725855, #11725856, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 274);