Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×#685 |
| Fitting | C2×C42×C5 ⋊ C2 |
| Sylow | C5 ⋊ C4×C22⋊C4 |
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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)(10,11,12,13)(15,17);(2,3)(4,5)(14,15)(16,17);(6,7,8,9)104 conjugacy classes — view the full character table.
| maximal subgroup of | #10598692, #10599408, #10599409, … |
| maximal normal subgroup of | #10598692, #10599408, #10599409, … |
| maximal quotient of | C4×#3937, #10600195, #10600198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 565);