Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C5 · Schur multiplier (H2) = C213 |
| direct product | C5×#62820 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
7382 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 6 generators on 29 points:
(1,2,3,4,5)(7,10)(11,13)(14,15)(16,22)(17,23)(18,21)(19,20)(24,28)(25,29)(26,27);(8,12)(11,13)(15,20)(16,23)(18,26)(25,28);(6,7)(8,11)(9,10)(12,13)(14,16)(15,17)(18,24)(19,23)(20,22)(21,25)(26,29)(27,28);(14,17)(15,16)(18,25)(19,22)(20,23)(21,24)(26,28)(27,29);(6,8)(7,11)(9,12)(10,13)(14,18,19,26)(15,21,20,27)(16,24,23,29)(17,25,22,28);(6,7)(8,11)(9,10)(12,13)(14,17)(15,16)(18,25)(19,22)(20,23)(21,24)(26,28)(27,29)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55808);