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×#36798 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1518 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(14,18)(17,19)(22,26)(25,27)(28,29,33,34)(30,37,40,35)(31,41,36,32)(38,39,42,43);(13,16)(17,19)(20,21,24,23)(22,25,26,27)(29,34)(31,36)(35,37)(38,42);(12,13)(14,17)(15,16)(18,19)(20,22)(21,25)(23,27)(24,26)(28,30,33,40)(29,35,34,37)(31,38,36,42)(32,39,41,43);(12,13)(14,17)(15,16)(18,19)(20,23,24,21)(22,27,26,25)(28,31,33,36)(29,32,34,41)(30,38,40,42)(35,39,37,43);(12,14)(13,17)(15,18)(16,19)(28,32)(29,36)(30,39)(31,34)(33,41)(35,42)(37,38)(40,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29786);