Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4054 |
| Fitting | C2×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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 — 4 generators on 15 points:
(3,4,6,7,5)(8,9,10,12,11,13,14,15);(1,2)(9,13)(12,15);(4,5)(6,7)(9,12)(10,14)(13,15);(1,2)62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599497, #10599519, #10599554, … |
| maximal normal subgroup of | #10599497, #10599519, #10599554, … |
| maximal quotient of | C2×#64991, C2×#64999, C2×#65000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1418);