Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#709 |
| Fitting | C2×C42×C5 ⋊ C2 |
| Sylow | C5 ⋊ C4×#41 |
310 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 159 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 — 4 generators on 17 points:
(1,2,4,5,3)(11,15)(14,17);(10,12,13,16)(11,14,15,17);(2,3)(4,5)(10,11)(12,14)(13,15)(16,17);(6,7,8,9)104 conjugacy classes — view the full character table.
| maximal subgroup of | #10599530, #10599571, C4×#3937, … |
| maximal normal subgroup of | #10599530, #10599571, C4×#3937, … |
| maximal quotient of | C4×#4018, C42×D20, C42×Dic10, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1146);