Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D5×#102 |
| Fitting | C5×#102 ⋊ C2 |
| Sylow | C5 ⋊ C2×#102 |
202 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 17 points:
(6,9)(7,12)(10,11)(13,14,16,17,15);(1,2,3,4)(5,6)(7,9)(8,11)(10,12);(14,15)(16,17)56 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 | D5×D4⋊C8, #10598961, #10598965, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 396);