Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#36698 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| socle | C23×C11 | C25 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
1484 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)(12,13)(14,17)(15,16)(18,19)(20,21)(22,24)(23,25)(26,27)(28,29,32,33)(30,34,37,40)(31,35,39,41)(36,42,38,43);(20,22,23,27)(21,24,25,26)(29,33)(34,40)(35,41)(42,43);(13,16)(17,19)(20,21)(22,26)(23,25)(24,27)(28,30,32,37)(29,34,33,40)(31,38,39,36)(35,43,41,42);(21,25)(24,26)(28,31,32,39)(29,35,33,41)(30,36,37,38)(34,42,40,43);(12,14,15,18)(13,17,16,19)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29686);