Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1284 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#7964 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #95 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | C2×#95 |
| prime radical | C24×C11 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C22×C42×C11 ◁ G | |
544 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,19,17,21,16,20)(14,22,23,18,25,26,24,27)(28,29)(30,36,38,42)(31,34)(32,35)(33,37,40,43)(39,41);(12,14,16,24,17,25,15,23)(13,18,19,26,21,27,20,22)(28,30)(29,33,35,40)(31,37)(32,38)(34,36,41,42)(39,43);(12,15,17,16)(13,19,21,20)(14,23,25,24)(18,26,27,22)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 952);