Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×(C2×AGL(1,𝔽5))⋊C4 |
| unambiguous semidirect product | D5⋊#95 |
| Fitting | C22×C4×C5 ⋊ C4 |
| Sylow | C5 ⋊ C2×#95 |
330 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 124 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 — 3 generators on 15 points:
(3,4)(5,6)(7,8,9,10)(11,12,13,15,14);(4,6)(12,13,14,15);(1,2)56 conjugacy classes — view the full character table.
| maximal subgroup of | #10598551, #10598552, #10598720, … |
| maximal normal subgroup of | #10598551, #10598552, #10598720, … |
| maximal quotient of | C2×#64863, C2×#64862, #10604165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1100);