Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2883 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C210 |
| direct product | C2×C11×#2889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C22×C11×2−1+4 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C11×#41 ◁ G | |
4770 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45);(3,4,7,12,8,11,20,25)(5,13,15,26,16,9,19,22)(6,10,18,24,17,23,30,33)(14,27,29,34,28,21,31,32);(3,5,8,16)(4,9,11,13)(6,14,17,28)(7,19,20,15)(10,21,23,27)(12,26,25,22)(18,31,30,29)(24,34,33,32);(3,6)(4,10)(5,14)(7,18)(8,17)(9,21)(11,23)(12,24)(13,27)(15,29)(16,28)(19,31)(20,30)(22,32)(25,33)(26,34);(6,17)(10,23)(14,28)(18,30)(21,27)(24,33)(29,31)(32,34)902 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53063);