Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #467 |
114 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,4,6,7,5,3)(9,11)(12,14,16,22)(13,17,19,26)(15,24,25,21)(18,27,23,20);(8,9)(10,11);(2,3)(4,5)(6,7)(9,11)(12,13,16,19)(14,20,22,27)(15,23,25,18)(17,24,26,21)Polycyclic presentation:
2^6,7|a^2=f,c^2=f,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^6,c^b=ce,d^c=df64 conjugacy classes — view the full character table.
| maximal subgroup of | #11737604, #11737608, #11737613, … |
| maximal normal subgroup of | #11737604, #11737608, #11737613, … |
| maximal quotient of | #11727266, #11727268, #11727273, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 585);