Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#23053 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C23×C11 | C23×C4 |
| prime radical | C24×C11 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
796 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(17,21)(22,23)(24,25,29,26,28,30,27,31);(16,17)(18,22)(19,23)(20,21)(24,26,29,30,28,31,27,25);(13,15)(16,18,20,19)(17,22,21,23)(24,27,28,29)(25,26,30,31);(16,19,20,18)(17,22,21,23)(24,27,28,29)(25,26,30,31)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16041);