Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #5450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#2375⋊C3 |
| unambiguous semidirect product | #2375⋊(C3×C5) |
| unambiguous semidirect product | (C5×#2375)⋊C3 |
| Fitting, Hall | C5×#2375 ⋊ C3 |
| derived | C24 ⋊ C2×C3×C4×C5 |
| Sylow | #2375 ⋊ C3×C5 |
316 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3,4,5)(10,12)(11,15)(13,25,14,20,21,19)(16,22,17,24,18,23);(6,7,8,9)(10,17,13,11)(12,24,20,22)(14,16,21,18)(15,19,23,25)170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236600);