Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D5×#103 |
| Fitting | C5×#103 ⋊ C2 |
| Sylow | C5 ⋊ C2×#103 |
162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 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:
(5,6,8,10)(7,12,11,9)(13,14,16,17,15);(1,2,3,4)(6,9)(7,11)(10,12);(14,15)(16,17)56 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#103, #10603984, #10603985, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#103, #10603984, #10603985, … |
| maximal quotient of | D5×Q8⋊C8, #10599025, #10599029, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 428);