Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#34416 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C2×C11×#538 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2522 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17)(18,22)(19,20)(21,23)(25,28)(26,30);(17,20)(21,22)(24,25,27,28)(26,29,30,31);(12,14,15,13)(24,25)(26,29)(27,28)(30,31);(16,17)(18,21)(19,20)(22,23)(24,25)(26,29)(27,28)(30,31);(16,18)(17,21)(19,23)(20,22)(24,26)(25,29)(27,30)(28,31)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27404);