Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #36702 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#36716 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C2×C11×#538 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2406 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(18,22)(21,23)(24,25)(26,33)(27,28)(29,37)(30,32)(31,38)(34,36)(35,39);(17,20)(21,23)(24,26,30,27)(25,28,32,33)(29,34,38,35)(31,36,37,39);(12,13)(14,15)(16,17)(18,21)(19,20)(22,23)(24,27,30,26)(25,28,32,33)(29,35,38,34)(31,36,37,39);(16,17)(18,21)(19,20)(22,23)(24,28)(25,26)(27,32)(29,36)(30,33)(31,34)(35,37)(38,39);(16,18)(17,21)(19,22)(20,23)(24,29)(25,31)(26,34)(27,35)(28,36)(30,38)(32,37)(33,39)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29704);