Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #463 |
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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)(14,19)(15,16)(17,18);(13,17)(14,18)(16,19);(2,3)(4,5)(6,7)(8,9,10,11)(13,16)(17,19)Polycyclic presentation:
2^6,7|a^2=e,d^2=f,c^a=cef,g^a=g^6,c^b=cd,d^b=df,d^c=df61 conjugacy classes — view the full character table.
| maximal subgroup of | #11737013, #11737014, #11737016, … |
| maximal normal subgroup of | #11737013, #11737014, #11737016, … |
| maximal quotient of | #11727908, #11727916, #11727920, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 687);