Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C7 ⋊ #482 |
106 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 39 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) = 224 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(10,14)(12,15)(17,22)(18,19)(21,23);(8,10)(9,12)(11,14)(13,15)(16,18,20,19)(17,21,23,22);(2,3)(4,5)(6,7)(8,9,11,13)(10,12,14,15)(16,17,20,23)(18,21,19,22)Polycyclic presentation:
2^6,7|a^2=e,b^2=f,d^2=f,c^a=cd,d^a=df,g^a=g^6,c^b=ce,d^c=df61 conjugacy classes — view the full character table.
| maximal subgroup of | #11737437, #11737438, #11737455, … |
| maximal normal subgroup of | #11737437, #11737438, #11737455, … |
| maximal quotient of | #11727257, #11727260, #11727261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 569);