Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#17386 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#538 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C4×D4×C11 ◁ G | |
1080 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)(12,13,15,20,17,21,26,34)(14,19,24,32,22,33,36,43)(16,18,25,29,27,30,39,41)(23,28,37,40,35,31,38,42);(13,18)(14,22)(15,25)(19,31)(21,30)(23,35)(24,38)(26,39)(28,33)(32,43)(36,37)(40,42);(12,14)(13,19)(15,24)(16,23)(17,22)(18,28)(20,32)(21,33)(25,37)(26,36)(27,35)(29,40)(30,31)(34,43)(38,39)(41,42);(14,23)(19,28)(22,35)(24,37)(31,33)(32,40)(36,38)(42,43)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 10374);