Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24475 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1324 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)(12,13,17,24,19,25,18,23)(14,26,30,39,31,41,29,20)(15,32,35,22,16,36,34,21)(27,37,33,40,42,43,28,38);(12,14)(13,20)(15,33)(16,28)(17,30)(18,29)(19,31)(21,40)(22,38)(23,41)(24,26)(25,39)(27,34)(32,43)(35,42)(36,37);(12,15,19,16)(13,21,25,22)(14,27,31,42)(17,34,18,35)(20,37,39,43)(23,32,24,36)(26,38,41,40)(28,29,33,30);(12,16,19,15)(13,22,25,21)(14,28,31,33)(17,34,18,35)(20,38,39,40)(23,32,24,36)(26,37,41,43)(27,29,42,30)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17463);