Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7943 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C2×C42 |
| direct product | C11×#7961 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#95 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C24×C11 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C42×C11 ◁ G | |
606 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17)(14,15)(18,19)(20,21)(22,30,33,34)(23,27)(24,28)(25,29)(26,32,35,31);(12,13,15,19,16,18,14,17)(20,22)(21,26,29,35)(23,31)(24,32)(25,33)(27,34,28,30);(13,18)(17,19)(20,23,25,24)(21,27,29,28)(22,31,33,32)(26,34,35,30)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 949);