Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#73113 |
| Fitting | C23×C5×C8 ⋊ D3 |
434 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4,5)(6,7,8,9)(10,11,13)(14,15,16,18,17,19,20,21);(11,12)(15,18)(16,20)(19,21)220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236535);