Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#34510 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C2×C11×#127 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2148 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17)(18,22)(19,23)(20,21)(24,25,30,28)(26,33,27,31)(29,36,37,32)(34,38,35,39);(17,21)(18,23)(24,26,30,27)(25,31,28,33)(29,34,37,35)(32,38,36,39);(16,18)(17,19)(20,23)(21,22)(24,27,30,26)(25,31,28,33)(29,35,37,34)(32,38,36,39);(12,14,15,13)(16,18)(17,19)(20,23)(21,22)(24,28,30,25)(26,31,27,33)(29,36,37,32)(34,38,35,39);(16,19)(17,18)(20,22)(21,23)(24,29,30,37)(25,32,28,36)(26,34,27,35)(31,38,33,39)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27498);