Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#4047 |
| Fitting | C22×C5×C8 ⋊ C2 |
| Sylow | C5 ⋊ C2×#131 |
266 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 266 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) = 23 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 4 generators on 23 points:
(3,4,6,7,5)(8,10,11,16,12,17,18,22)(9,14,15,21,13,19,20,23);(1,2)(9,13)(14,19)(15,20)(21,23);(4,5)(6,7)(8,9)(10,14)(11,15)(12,13)(16,21)(17,19)(18,20)(22,23);(1,2)104 conjugacy classes — view the full character table.
| maximal subgroup of | #10599487, #10599488, #10599741, … |
| maximal normal subgroup of | #10599487, #10599488, #10599741, … |
| maximal quotient of | C2×C8×Dic10, C2×#64968, #10610176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1410);