Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11086 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #124 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #397 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
866 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)(16,17,21,27,22,25,20,26)(18,23,31,39,29,40,30,38)(19,32,36,42,34,24,35,43)(28,37,45,46,44,47,33,41);(12,13)(14,15)(16,18)(17,23)(19,33,34,45)(20,30)(21,31)(22,29)(24,41,32,46)(25,40)(26,38)(27,39)(28,35,44,36)(37,42,47,43);(13,15)(16,19)(17,24)(18,28)(20,36)(21,35)(22,34)(23,37)(25,32)(26,43)(27,42)(29,44)(30,45)(31,33)(38,46)(39,41)(40,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4074);