Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#26196 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C5 |
| prime radical | C2×C5×#135 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C4×C5 ◁ G | |
742 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3,4,5)(6,7)(8,11)(9,13)(10,12)(14,15)(16,25)(17,27)(18,21)(19,24)(20,23)(22,29)(26,28);(6,8,10,9)(7,11,12,13)(14,16)(15,18)(17,23)(19,27)(20,26)(21,29)(22,28)(24,25);(6,9,10,8)(7,11,12,13)(14,17)(15,21)(16,24)(18,20)(19,28)(22,26)(23,27)(25,29);(14,18)(15,16)(17,20)(19,28)(21,24)(22,27)(23,26)(25,29)215 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 19184);