Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23876 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#24086 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C5 |
| prime radical | C5×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G | |
1014 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)(8,13)(9,11)(10,12)(14,15)(16,24)(17,22)(18,21)(19,23)(20,26)(25,29)(27,28);(6,8,10,9)(7,11,12,13)(14,16)(15,20)(17,26)(18,27)(19,25)(21,29)(22,24)(23,28);(6,9,10,8)(7,11,12,13)(15,21)(16,25)(18,19)(22,23)(26,27)(28,29);(7,12)(11,13)(15,22)(20,24)(21,23)(28,29)215 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 17074);