Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#20964 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#120 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C2×#386 |
| prime radical | C11×#3449 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
1700 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)(12,13,16,21,17,20,29,34)(14,18,24,32,23,31,38,42)(15,25,27,35,26,19,28,33)(22,30,37,41,36,40,39,43);(12,14,16,24,17,23,29,38)(13,18,21,32,20,31,34,42)(15,22,28,39,26,36,27,37)(19,30,35,43,25,40,33,41);(12,15)(13,19)(14,22)(16,28)(17,26)(18,30)(20,25)(21,35)(23,36)(24,39)(27,29)(31,40)(32,43)(33,34)(37,38)(41,42);(13,20)(18,31)(19,25)(21,34)(30,40)(32,42)(33,35)(41,43)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13952);