Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#21483 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C11 | #120 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C4×#120 |
| prime radical | C11×#3025 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C11 ◁ C22×C8×C11 ◁ G | |
1328 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)(12,13,17,22,18,16,21,30)(14,19,26,33,25,24,32,39)(15,20,29,35,28,27,34,40)(23,36,38,43,37,31,41,42);(12,14)(13,19)(15,23)(16,24)(17,26)(18,25)(20,31)(21,32)(22,33)(27,36)(28,37)(29,38)(30,39)(34,41)(35,42)(40,43);(12,15)(13,20)(14,23)(16,27)(17,29)(18,28)(19,31)(21,34)(22,35)(24,36)(25,37)(26,38)(30,40)(32,41)(33,42)(39,43);(12,16,17,30,18,13,21,22)(14,24,26,39,25,19,32,33)(15,27,29,40,28,20,34,35)(23,36,38,43,37,31,41,42)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14471);