Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #421 |
154 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 67 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)(8,10)(9,14)(11,19)(12,21)(13,18)(15,23)(16,22)(17,20);(10,18)(14,22)(17,23)(19,21);(2,3)(4,5)(6,7)(8,9,11,15,13,16,12,20)(10,17,19,14,18,23,21,22)Polycyclic presentation:
2^6,7|a^2=d,d^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^6,c^b=cf,e^c=ef82 conjugacy classes — view the full character table.
| maximal subgroup of | #11727759, #11727766, #11727792, … |
| maximal normal subgroup of | #11727759, #11727766, #11727792, … |
| maximal quotient of | #11729328, #11729344, #11729351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 770);