Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#4131 |
| Sylow | C5 ⋊ C2×#131 |
266 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 140 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:
(1,2)(3,4,5,7,6)(8,10)(9,13)(11,17)(12,16)(14,20)(15,19)(18,22)(21,23);(10,16)(13,19)(17,22)(20,23);(4,5,6,7)(8,9,11,14,12,15,18,21)(10,13,17,20,16,19,22,23);(1,2)50 conjugacy classes — view the full character table.
| maximal subgroup of | #10603920, #10603926, #10603959, … |
| maximal normal subgroup of | #10603920, #10603926, #10603959, … |
| maximal quotient of | C2×#65691, C2×#65696, C2×#65697, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1593);