Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4⋊C4×AGL(1,𝔽5) |
| Fitting | C5×C4⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ C4×C4⋊C4 |
194 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 13 points:
(2,3,4,5);(1,2,3,5,4)(10,11,12,13);(6,7,8,9)(11,13)50 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#102, #10603952, #10603953, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#102, #10603952, #10603953, … |
| maximal quotient of | #10603779, #10603780, #10603781, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1048);