Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2069 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11251 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #396 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1441 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
620 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,24)(15,29,32,37)(16,22)(17,21)(18,23)(19,26)(20,31,38,33)(25,41,43,34)(27,35)(28,39)(30,36,42,40);(12,14,16,26,18,28,17,27)(13,19,21,24,23,35,22,39)(15,30,31,25,32,42,33,43)(20,36,37,34,38,40,29,41);(12,15,16,31,18,32,17,33)(13,20,21,37,23,38,22,29)(14,25,26,42,28,43,27,30)(19,34,24,40,35,41,39,36)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4239);