Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2127 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#12589 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#99 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C2×#41 | C23×C11 |
| socle | C2×C11 | C2×#342 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C22×C11×#41 ◁ G | |
752 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)(14,22,23,34)(15,26,27,19)(16,29)(17,21)(18,24)(20,30)(25,39,37,35)(28,33,41,40)(31,36)(32,43)(38,42);(12,14,16,25,17,23,30,37)(13,18,20,32,21,31,29,42)(15,24,28,38,27,36,41,43)(19,22,33,35,26,34,40,39);(14,23)(18,31)(22,34)(24,36)(25,37)(32,42)(35,39)(38,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5577);