Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×C22⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #518 |
338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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) = 80 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2,4,5,3)(6,7,8,9)(12,16)(14,17);(11,15)(14,17);(10,12)(11,14)(13,16)(15,17);(2,3)(4,5)(10,11)(12,14)(13,15)(16,17)Polycyclic presentation:
2^6,5|d^2=e,c^a=cf,g^a=g^4,d^b=df74 conjugacy classes — view the full character table.
| maximal subgroup of | #10599753, #10599754, #10599755, … |
| maximal normal subgroup of | #10599753, #10599754, #10599755, … |
| maximal quotient of | #10605053, #10605064, #10605065, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1158);