Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #58990 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#60023 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C2×C11×#121 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1728 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,16)(14,18,19,17)(20,21)(22,23)(24,26)(25,27);(13,16)(17,18)(20,22,24,27)(21,23,26,25)(30,34)(32,35);(12,13)(14,17)(15,16)(18,19)(20,21,24,26)(22,25,27,23)(28,29,31,33)(30,32,34,35);(12,13)(14,17)(15,16)(18,19)(20,22)(21,25)(23,26)(24,27)(28,30,31,34)(29,32,33,35);(12,14)(13,17)(15,19)(16,18)(20,23,24,25)(21,22,26,27)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53011);