Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#4039 |
| Fitting | C2×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 175 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:
(1,2)(3,4,5,6)(8,10)(11,12,14,15,13);(1,2)(7,8,9,10);(8,10)(12,13)(14,15);(1,2)80 conjugacy classes — view the full character table.
| maximal subgroup of | #10598936, #10598938, #10599573, … |
| maximal normal subgroup of | #10598936, #10598938, #10599573, … |
| maximal quotient of | C2×#64955, C2×#64943, C2×#64958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1175);