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×#60022 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C11×#2678 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1968 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(17,18)(20,21)(22,26)(23,27)(24,25)(28,29)(30,31)(32,34)(33,35);(12,13,16,15)(14,18,19,17)(21,25)(22,27)(28,30,32,35)(29,31,34,33);(20,22)(21,23)(24,27)(25,26)(28,29,32,34)(30,33,35,31);(12,14,16,19)(13,17,15,18)(20,22)(21,23)(24,27)(25,26)(28,30)(29,33)(31,34)(32,35);(12,15,16,13)(14,18,19,17)(20,23)(21,22)(24,26)(25,27)(28,31,32,33)(29,30,34,35)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53010);