Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4008 |
| Fitting | C2×C5×D4 ⋊ C4 |
| Sylow | C5 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 52 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:
(3,4,5,7,6)(8,9)(10,12)(11,14)(13,15);(4,5,6,7)(8,9,10,12,11,14,15,13);(1,2)38 conjugacy classes — view the full character table.
| maximal subgroup of | #10603924, #10603955, #10603956, … |
| maximal normal subgroup of | #10603924, #10603955, #10603956, … |
| maximal quotient of | C2×#64869, #10604259, C2×#64870, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1106);