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) = C27×C4 |
| direct product | C11×#34177 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C25×C11 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2446 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 704 |
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)(18,22)(20,23)(24,25)(26,30)(27,34)(28,29)(31,35)(32,38)(33,36)(37,39);(16,17,19,21)(18,20,22,23)(25,29)(30,36)(31,34)(37,38);(16,18)(17,20)(19,22)(21,23)(24,26,28,33)(25,30,29,36)(27,32,35,39)(31,37,34,38);(24,25)(26,30)(27,31)(28,29)(32,37)(33,36)(34,35)(38,39);(24,27)(25,31)(26,32)(28,35)(29,34)(30,37)(33,39)(36,38)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27165);