Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12503 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22×C8 |
| direct product | C5×#12515 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C5 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C42×C5 ◁ C5×C82 ◁ G | |
398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5)(7,10)(8,11)(12,13)(15,19)(16,20)(17,23)(21,29)(22,27)(24,28)(25,26);(14,15,20,26,17,21,24,27,18,22,28,29,23,25,16,19);(6,7,11,13,9,12,8,10)350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 5503);