Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#21006 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,21,27,22,26,20,25)(18,23,31,38,30,39,29,37)(19,32,33,24,34,40,35,41)(28,42,43,36,45,46,44,47);(16,18,20,31,22,30,21,29)(17,23,27,37,26,39,25,38)(19,28,33,44,34,45,35,43)(24,36,32,46,41,47,40,42);(13,15)(16,19)(17,24)(18,28)(20,33)(21,35)(22,34)(23,36)(25,40)(26,41)(27,32)(29,43)(30,45)(31,44)(37,46)(38,42)(39,47);(16,20,22,21)(17,25,26,27)(18,29,30,31)(19,33,34,35)(23,37,39,38)(24,40,41,32)(28,43,45,44)(36,46,47,42)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13994);