Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9103 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#10990 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1278 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,21,25,22,26,20,35)(18,27,29,23,30,39,36,38)(19,31,33,42,34,24,32,41)(28,44,45,37,46,43,47,40);(16,18)(17,23)(19,28)(20,36)(21,29)(22,30)(24,40)(25,39)(26,38)(27,35)(31,37)(32,47)(33,45)(34,46)(41,44)(42,43);(13,15)(16,19,22,34)(17,24,26,31)(18,28,30,46)(20,33,21,32)(23,37,38,40)(25,42,35,41)(27,43,39,44)(29,47,36,45)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3978);