Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33359 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33370 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×#99 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C2×Q8 | C24×C11 |
| prime radical | C11×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×D4×C11 ◁ C2×C11×2−1+4 ◁ G | |
1208 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,21,17,22,29,36)(14,19,25,34,23,32,38,42)(15,20,27,35,26,18,28,31)(24,33,39,43,37,30,40,41);(13,18)(15,26)(19,30)(20,22)(21,35)(24,37)(27,28)(31,36)(32,33)(34,43)(39,40)(41,42);(12,14)(13,19)(15,24)(16,25)(17,23)(18,30)(20,33)(21,34)(22,32)(26,37)(27,39)(28,40)(29,38)(31,41)(35,43)(36,42);(14,23)(19,32)(24,37)(25,38)(30,33)(34,42)(39,40)(41,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26358);