Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1705 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#8817 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | #127 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2816 |
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)(18,24)(19,28)(20,22)(21,26)(23,25)(27,30)(29,31)(32,33)(34,40)(35,37)(36,44)(38,42)(39,43)(41,46)(45,47);(16,18,25,31,20,27,19,26)(17,21,28,30,22,29,23,24)(33,37)(38,45)(39,44)(40,46);(17,22)(21,29)(23,28)(24,30)(32,34,36,42,35,41,43,47)(33,38,39,40,37,45,44,46)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1805);