Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2221 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13073 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #466 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#131 ◁ G | |
478 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)(16,17,21,26,23,19,22,34)(18,27,31,44,32,43,39,45)(20,35,37,33,28,46,38,25)(24,40,41,30,29,47,42,36);(16,18,28,30,22,31,37,47,23,32,20,36,21,39,38,40)(17,24,25,43,26,42,35,44,19,29,33,27,34,41,46,45);(13,15)(16,19)(17,23)(18,29)(20,25)(21,26)(22,34)(24,32)(27,30)(28,33)(31,41)(35,38)(36,43)(37,46)(39,42)(40,44)(45,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6061);