Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C27×C4 |
| direct product | C11×#34369 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C2×C11×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2410 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(17,20)(18,22)(24,25,28,29)(26,32,33,30)(27,35,36,31)(34,37,39,38);(17,20)(21,23)(25,29)(26,33)(31,35)(34,39);(16,17,19,20)(18,21,22,23)(24,25)(26,30)(27,31)(28,29)(32,33)(34,37)(35,36)(38,39);(16,18)(17,21)(19,22)(20,23)(24,26,28,33)(25,30,29,32)(27,34,36,39)(31,37,35,38);(24,27,28,36)(25,31,29,35)(26,34,33,39)(30,37,32,38)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27357);