Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#104 ⋊ C2 |
| Sylow | C7 ⋊ #444 |
104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 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)(8,11,12,21,13,20,22,10)(9,15,16,23,18,14,17,19);(8,10)(9,14)(11,12)(13,21)(15,18)(16,19)(17,23)(20,22);(2,3)(4,5)(6,7)(8,9)(10,19)(11,15)(12,16)(13,18)(14,20)(17,22)(21,23)Polycyclic presentation:
2^6,7|c^2=d,d^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^6,c^b=ce,e^b=ef,e^c=ef64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89595, #11736425, #11736434, … |
| maximal normal subgroup of | C2×#89595, #11736425, #11736434, … |
| maximal quotient of | #11725904, #11725905, #11725906, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 357);