Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C5×SD16 ⋊ C2 |
| Sylow | C5 ⋊ #496 |
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 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)(7,9)(11,16)(12,15)(14,17);(10,11,15,16,13,17,12,14);(2,3)(4,5)(6,7)(8,9)(11,14)(12,15)(16,17)Polycyclic presentation:
2^6,5|b^2=ef,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^4,c^b=ce,e^c=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | #10611372, #10611373, #10611395, … |
| maximal normal subgroup of | #10611372, #10611373, #10611395, … |
| maximal quotient of | #10600953, #10600974, #10600984, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 803);