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×#60004 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C11×#2535 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1808 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)(14,18)(15,17)(16,19)(21,26)(24,27)(29,33)(30,35);(12,13,15,17)(14,16,19,18)(20,21,25,26)(22,27,23,24)(29,33)(30,35);(20,22,25,23)(21,27,26,24)(28,29,32,33)(30,34,35,31);(12,13)(14,16)(15,17)(18,19)(20,23,25,22)(21,24,26,27)(28,30)(29,34)(31,33)(32,35);(12,14)(13,16)(15,19)(17,18)(20,24)(21,22)(23,26)(25,27)(28,31,32,34)(29,30,33,35)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 52992);