Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #36702 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#36767 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C11×#2703 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1650 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)(14,18)(17,19)(21,25)(22,23)(30,34)(32,35);(13,16)(17,19)(20,21,24,25)(22,26,23,27)(28,29,31,33)(30,32,34,35);(12,13)(14,17)(15,16)(18,19)(20,22,24,23)(21,26,25,27)(28,30,31,34)(29,32,33,35);(12,13)(14,17)(15,16)(18,19)(20,21)(22,26)(23,27)(24,25);(12,14)(13,17)(15,18)(16,19)(20,23,24,22)(21,27,25,26)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29755);