Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#85549 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22×C5 | #1020 |
| commutator, cosocle, hypocenter | #543⋊C3 | C2×C5 |
| Frattini | C22 | C5×#1020 |
| Fitting | C5×#543 | D3 |
| prime radical | C5×#543⋊C3 | C2 |
| LCS | G ▷ #543⋊C3 | |
| UCS | C1 ◁ C22×C5 | |
248 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3,4,5)(6,7,10,12)(8,9,11,13)(14,25,26,22,18,19,23,20)(15,16,29,17,21,24,28,27);(7,8,10)(11,12,13)(16,23,17)(19,28,20)(22,25,29)(24,26,27)105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236985);