Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4010 |
| Fitting | C2×C5×Q8 ⋊ 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)(8,10,13,9)(11,15,12,14);(4,5,6,7)(8,9,11,14,13,10,12,15);(1,2)38 conjugacy classes — view the full character table.
| maximal subgroup of | #10603930, #10603987, #10603988, … |
| maximal normal subgroup of | #10603930, #10603987, #10603988, … |
| maximal quotient of | C2×#64868, #10604258, C2×#64870, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1121);