Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#12881 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #117 |
| commutator | C2×C4 | C22×C8×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C22×C11 | #432 |
| prime radical | C23×C11 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C11×#97 ◁ G | |
298 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)(13,14)(16,17,20,27,21,24,36,40,22,25,35,41,19,26,33,42)(18,28,30,43,31,38,45,47,32,23,34,39,29,37,44,46);(12,13,15,14)(16,18,19,29,22,32,21,31)(17,23,26,38,25,28,24,37)(20,34,33,45,35,30,36,44)(27,43,42,46,41,39,40,47);(12,14,15,13)(17,24,25,26)(20,35)(23,37,28,38)(27,42,41,40)(30,34)(33,36)(39,47,43,46)(44,45)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5869);