Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#34234 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C2×C11×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2214 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)(12,13,15,14)(17,20)(21,23)(24,25)(26,32)(27,35)(28,29)(30,34)(31,36)(33,37)(38,39);(12,14,15,13)(25,29)(30,32)(31,35)(37,38);(16,17)(18,21)(19,20)(22,23)(24,26,28,34)(25,30,29,32)(27,33,36,39)(31,37,35,38);(24,25)(26,30)(27,31)(28,29)(32,34)(33,37)(35,36)(38,39);(16,18,19,22)(17,21,20,23)(24,27)(25,31)(26,33)(28,36)(29,35)(30,37)(32,38)(34,39)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27222);