Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9914 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#9965 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C5 |
| prime radical | C2×C5×#121 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G | |
830 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5)(6,7)(8,9)(10,11)(12,14)(13,15)(16,17)(18,19,22,26)(20,27,30,28)(21,32,23,25)(24,31,33,29);(14,17)(18,20,22,30)(19,24,26,33)(21,31,23,29)(25,28,32,27);(7,9)(10,12)(11,14)(13,16)(15,17)(18,19)(20,28)(21,25)(22,26)(23,32)(24,29)(27,30)(31,33)200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 2953);