Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#101 ⋊ C2 |
| Sylow | C7 ⋊ #471 |
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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)(8,11,13,20)(9,14,16,17)(10,15,18,23)(12,21,22,19);(8,10,12,17,13,18,22,14)(9,11,15,19,16,20,23,21);(2,3)(4,5)(6,7)(8,9)(10,11)(12,15)(13,16)(14,21)(17,19)(18,20)(22,23)Polycyclic presentation:
2^6,7|b^2=d,c^2=f,d^2=f,c^a=cde,e^a=ef,g^a=g^6,c^b=ce,e^b=ef,d^c=df49 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89526, #11736157, #11736164, … |
| maximal normal subgroup of | C2×#89526, #11736157, #11736164, … |
| maximal quotient of | #11726194, #11726196, #11726200, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 288);