Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×D5×C22⋊C4 |
| Fitting | C2×C5×C22⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ C22×C22⋊C4 |
674 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 207 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 4 generators on 15 points:
(3,4)(5,6)(7,8)(9,10)(11,12,14,15,13);(4,6)(7,8,9,10);(1,2)(12,13)(14,15);(1,2)80 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#323, #10598913, D5×#342, … |
| maximal normal subgroup of | D5×#323, #10598913, D5×#342, … |
| maximal quotient of | C2×#64955, C2×#64935, C2×D5×#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1156);