Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C5×SD16 ⋊ C2 |
| Sylow | C5 ⋊ #449 |
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 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) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,4,5,3)(10,11,13,14)(12,17,16,15);(7,9)(11,15)(12,16)(14,17);(2,3)(4,5)(6,7)(8,9)(11,14)(15,17)Polycyclic presentation:
2^6,5|c^2=f,d^2=f,b^a=be,c^a=cf,g^a=g^4,c^b=cd,d^b=df,d^c=df47 conjugacy classes — view the full character table.
| maximal subgroup of | #10611410, #10611412, #10611415, … |
| maximal normal subgroup of | #10611410, #10611412, #10611415, … |
| maximal quotient of | #10600957, #10600994, #10600997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 799);