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×#2884 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C22×C11×2−1+4 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×Q8×C11 ◁ G | |
4818 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)(5,13,16,9)(6,10)(7,11)(8,12)(14,27,30,21)(15,28,32,22)(17,23)(18,24)(19,25)(20,26)(29,34,31,33);(3,5)(4,9)(6,14)(7,15)(8,16)(10,21)(11,22)(12,13)(17,29)(18,30)(19,31)(20,32)(23,33)(24,27)(25,34)(26,28);(3,6,8,18)(4,10,12,24)(5,14,16,30)(7,19,20,17)(9,21,13,27)(11,25,26,23)(15,31,32,29)(22,34,28,33);(3,7,8,20)(4,11,12,26)(5,15,16,32)(6,17,18,19)(9,22,13,28)(10,23,24,25)(14,29,30,31)(21,33,27,34)902 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53057);