Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23914 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3485 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1706 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)(16,17,21,25)(18,22,27,37)(19,29,30,41)(20,32,35,24)(23,34,39,31)(26,42,43,46)(28,40,33,38)(36,45,47,44);(12,13)(14,15)(16,18,21,27)(17,22,25,37)(19,26,30,43)(20,33,35,28)(23,36,39,47)(24,40,32,38)(29,46,41,42)(31,45,34,44);(13,15)(16,19)(17,23)(18,26)(20,34)(21,30)(22,36)(24,41)(25,39)(27,43)(28,45)(29,32)(31,35)(33,44)(37,47)(38,46)(40,42);(18,27)(20,35)(22,37)(24,32)(26,43)(29,41)(31,34)(36,47)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16902);