Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26 |
| direct product | C5×#23980 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C5 |
| prime radical | C22×C5×D4 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C2×C4×C5×D4 ◁ G | |
1222 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5)(6,7)(8,9)(10,11)(12,16)(13,15)(14,17)(18,19,24,27)(20,22,26,23)(21,29,33,28)(25,32,30,31);(10,12,13,17)(11,14,15,16)(18,20)(19,22)(21,30)(23,27)(24,26)(25,33)(28,32)(29,31);(7,9)(18,21,24,33)(19,25,27,30)(20,28,26,29)(22,32,23,31);(11,15)(14,16)(18,22,24,23)(19,26,27,20)(21,31,33,32)(25,28,30,29)230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 16968);