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×#36745 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2184 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)(13,15)(18,22)(21,23)(24,25)(26,27)(28,32)(29,30)(31,35)(33,34)(36,37)(38,39);(17,20)(21,23)(25,30)(26,31)(32,37)(33,38);(12,13,14,15)(16,17)(18,21)(19,20)(22,23)(24,26,29,31)(25,27,30,35)(28,33,36,38)(32,34,37,39);(16,17)(18,21)(19,20)(22,23)(24,27)(25,31)(26,30)(28,34)(29,35)(32,38)(33,37)(36,39);(16,18)(17,21)(19,22)(20,23)(24,28,29,36)(25,32,30,37)(26,33,31,38)(27,34,35,39)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29733);