Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11134 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #397 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
838 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17,21,25,22,26,20,27)(18,28,32,40,31,39,30,23)(19,33,36,43,37,24,35,42)(29,41,45,38,44,46,34,47);(12,13)(14,15)(16,18,20,30,22,31,21,32)(17,23,25,28,26,40,27,39)(19,34,35,44,37,45,36,29)(24,41,42,38,33,46,43,47);(13,15)(16,19,22,37)(17,24,26,33)(18,29,31,44)(20,36,21,35)(23,38,40,47)(25,43,27,42)(28,41,39,46)(30,45,32,34)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4122);