Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#12563 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #106 |
| commutator | C8 | C2×C42×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C22×C11 | C2×#106 |
| prime radical | C24×C11 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G | |
570 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)(18,29,32,42)(19,25)(20,37)(21,38)(22,39)(23,28)(24,31,41,33)(26,36)(27,35)(30,43,34,47)(40,45,44,46);(13,15)(16,18,21,33,22,34,35,45,23,32,20,31,19,30,36,46)(17,24,27,42,25,40,38,47,28,41,26,29,39,44,37,43);(16,19,23,22)(17,25,28,39)(18,30,32,34)(20,35,21,36)(24,40,41,44)(26,37,27,38)(29,43,42,47)(31,45,33,46)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5551);