Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#21080 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#121 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C2×#388 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
1000 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,21,18,22,16,32)(14,23,27,34,25,37,26,19)(15,28,31,43,30,20,29,35)(24,38,41,33,39,36,40,42);(12,14)(13,19,22,34)(15,24)(16,26)(17,27)(18,25)(20,33,28,42)(21,23,32,37)(29,40)(30,39)(31,41)(35,36,43,38);(12,15,16,29,18,30,17,31)(13,20,21,35,22,28,32,43)(14,24,26,40,25,39,27,41)(19,33,23,36,34,42,37,38);(14,25)(19,34)(23,37)(24,39)(26,27)(33,42)(36,38)(40,41)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14068);