Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #127⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C8 · Schur multiplier (H2) = C4 |
| direct product | C5×#1842⋊C3 |
| unambiguous semidirect product | #1842⋊(C3×C5) |
| unambiguous semidirect product | (C5×#1842)⋊C3 |
| Fitting, Hall | C5×#1842 ⋊ C3 |
| derived | C42 ⋊ C3×C5×C8 |
| Sylow | #1842 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C5 | #127⋊C3 |
| commutator, hypocenter | C42 | C3×C5×C8 |
| Frattini | C22×C4 | C2×C5×A4 |
| Fitting | C5×#1842 | C3 |
| socle | C23×C5 | C4×A4 |
| prime radical | C2×C5×C42⋊C3 | C4 |
| cosocle | C43 | C2×C3×C5 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C4×C5 | |
140 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 30 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)(6,7,8,10,9,11,12,13)(14,15,18,17,19,22)(16,25,23)(20,24,21);(14,16,17,21)(15,20,19,25)(18,22)(23,24)200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236387);