Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #385 |
234 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,7,5,3)(8,10,11,9)(13,15)(17,19);(16,17)(18,19);(2,3)(4,5)(6,7)(8,9,11,10)(12,13)(14,15)Polycyclic presentation:
2^6,7|a^2=f,c^2=f,c^a=cd,g^a=g^6,c^b=ce88 conjugacy classes — view the full character table.
| maximal subgroup of | #11725252, #11725253, #11726711, … |
| maximal normal subgroup of | #11725252, #11725253, #11726711, … |
| maximal quotient of | #11727160, #11727169, #11727174, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 480);