Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #461 |
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 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)(9,11)(12,13,15,17)(14,19,18,16);(13,16)(14,18)(17,19);(2,3)(4,5)(6,7)(8,9,10,11)Polycyclic presentation:
2^6,7|a^2=e,c^2=f,d^2=f,c^a=ce,g^a=g^6,c^b=cd,d^b=df,d^c=df61 conjugacy classes — view the full character table.
| maximal subgroup of | #11737064, #11737065, #11737073, … |
| maximal normal subgroup of | #11737064, #11737065, #11737073, … |
| maximal quotient of | #11727907, #11727919, #11727925, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 696);