Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9263 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#9263 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C11×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
478 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,18,20,27)(14,22,24,41)(15,26)(21,33,32,42)(23,40,28,25)(30,39)(31,38)(34,35);(12,13,15,27,29,32,39,33)(14,19,28,34,40,43,22,38)(16,21,26,42,17,20,30,18)(23,31,25,36,41,35,24,37);(12,14)(13,19)(15,28)(16,25)(17,24)(18,31)(20,37)(21,36)(22,39)(23,30)(26,41)(27,34)(29,40)(32,43)(33,38)(35,42)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2251);