Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33348 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33351 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×#99 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C2×D4 | C24×C11 |
| prime radical | C11×#3487 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×Q8×C11 ◁ C2×C11×2−1+4 ◁ G | |
1212 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)(17,31,32,22)(18,23)(19,26,34,30)(25,35)(27,40,41,36)(28,37)(29,38)(33,39,43,42);(12,14,18,16)(13,19,23,34)(15,25,28,29)(17,26,32,30)(20,33,37,43)(21,22,24,31)(27,39,41,42)(35,40,38,36);(12,15,18,28)(13,20,23,37)(14,25,16,29)(17,27,32,41)(19,33,34,43)(21,38,24,35)(22,36,31,40)(26,39,30,42);(12,16,18,14)(13,21,23,24)(15,25,28,29)(17,30,32,26)(19,22,34,31)(20,35,37,38)(27,39,41,42)(33,40,43,36)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26339);