Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×D20 |
| Fitting | C2×C42×C5 ⋊ C2 |
| Sylow | C5 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 183 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) = 160 |
A minimal faithful permutation representation — 4 generators on 15 points:
(3,4,5,6)(11,12,14,15,13);(1,2)(4,6)(12,13)(14,15);(7,8,9,10);(1,2)104 conjugacy classes — view the full character table.
| maximal subgroup of | #10599461, #10599462, #10599463, … |
| maximal normal subgroup of | #10599461, #10599462, #10599463, … |
| maximal quotient of | C42×D20, #10605030, C4×#4021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1145);