Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #34980 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C28×C4 |
| direct product | C5×#35317 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| prime radical | C2×C5×#532 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
3406 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2,3,4,5)(7,9)(11,12)(14,15,19,22)(16,17,20,25)(18,26,27,21)(23,29,28,24);(10,11,13,12)(14,16)(15,17)(18,23)(19,20)(21,24)(22,25)(26,29)(27,28);(6,7,8,9)(10,12,13,11)(14,17)(15,20)(16,22)(18,24)(19,25)(21,28)(23,26)(27,29);(14,17)(15,20)(16,22)(18,24)(19,25)(21,28)(23,26)(27,29);(14,18,19,27)(15,21,22,26)(16,23,20,28)(17,24,25,29)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 28305);