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) = C25 |
| direct product | C11×#11137 |
| 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 | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
854 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)(12,13)(14,15)(16,17,21,25,22,26,20,35)(18,27,31,38,30,43,29,23)(19,24,33,41,34,40,36,39)(28,42,44,47,32,46,45,37);(16,18,20,29,22,30,21,31)(17,23,25,27,26,38,35,43)(19,32,33,45,34,28,36,44)(24,37,39,46,40,47,41,42);(13,15)(16,19)(17,24)(18,28)(20,36)(21,33)(22,34)(23,37)(25,41)(26,40)(27,42)(29,45)(30,32)(31,44)(35,39)(38,47)(43,46)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4125);