Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11297 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #385 |
| prime radical | C24×C11 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
578 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)(16,17,21,26,22,27,20,25)(18,28,31,23,32,38,30,39)(19,33,34,24,36,40,35,41)(29,43,44,47,45,37,46,42);(12,13)(14,15)(16,18,20,31,22,32,21,30)(17,23,25,38,27,39,26,28)(19,29,35,44,36,45,34,46)(24,37,33,42,41,43,40,47);(13,15)(16,19,20,34,22,36,21,35)(17,24,25,40,27,41,26,33)(18,29,30,44,32,45,31,46)(23,37,28,42,39,43,38,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4285);