Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26 |
| direct product | C5×#24400 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C5 |
| prime radical | C22×C5×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G | |
1322 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5)(6,7)(8,9)(10,11,14,19,16,21,15,20)(12,17,23,32,24,33,30,37)(13,25,27,36,29,35,28,18)(22,34,26,40,38,41,39,31);(7,9)(10,12)(11,17)(13,26)(14,23)(15,30)(16,24)(18,34)(19,32)(20,37)(21,33)(22,28)(25,40)(27,38)(29,39)(31,35)(36,41);(10,13,16,29)(11,18,21,36)(12,22,24,38)(14,28,15,27)(17,31,33,40)(19,35,20,25)(23,39,30,26)(32,41,37,34);(7,9)215 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 17388);