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×#36774 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C11×#2635 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1574 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)(24,27)(28,29,33,30)(31,36,39,34)(32,35,40,37)(38,42,43,41);(13,16)(17,19)(20,21,23,25)(22,24,26,27)(29,30)(34,36)(35,37)(41,42);(12,13)(14,17)(15,16)(18,19)(20,22,23,26)(21,24,25,27)(28,30,33,29)(31,36,39,34)(32,37,40,35)(38,42,43,41);(12,13)(14,17)(15,16)(18,19)(28,31,33,39)(29,34,30,36)(32,38,40,43)(35,41,37,42);(12,14)(13,17)(15,18)(16,19)(28,32,33,40)(29,35,30,37)(31,38,39,43)(34,41,36,42)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29762);