Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#8149 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C11 | C23 |
| commutator | C23 | C2×C42×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C23×C11 | C2×C42 |
| prime radical | C24×C11 | C42 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C11 ◁ G | |
554 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,20,22,19,18,21,23)(24,25,27,26,28,29,31,30);(13,15)(17,18)(22,23)(24,25,27,26,28,29,31,30);(16,18,20,23,19,17,21,22)(24,26,27,29,28,30,31,25)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1137);