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×#33362 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×#99 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C2×D4 | C24×C11 |
| prime radical | C11×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×Q8×C11 ◁ C2×C11×2−1+4 ◁ G | |
1220 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)(14,24)(15,20)(16,21)(17,22,31,33)(18,23)(19,26,34,30)(25,35)(27,36,41,43)(28,37)(29,38)(32,39,42,40);(12,14,18,16)(13,19,23,34)(15,25,28,29)(17,30,31,26)(20,32,37,42)(21,33,24,22)(27,40,41,39)(35,36,38,43);(12,15,18,28)(13,20,23,37)(14,25,16,29)(17,27,31,41)(19,32,34,42)(21,38,24,35)(22,36,33,43)(26,39,30,40);(12,16,18,14)(13,21,23,24)(15,25,28,29)(17,30,31,26)(19,33,34,22)(20,35,37,38)(27,39,41,40)(32,36,42,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26350);