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×#34237 |
| 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 | |
2186 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)(26,31)(27,32)(28,36)(29,30)(33,37)(34,35)(38,39);(12,14,15,13)(25,30)(27,31)(33,36)(35,38);(16,17)(18,21)(19,20)(22,23)(24,26,29,32)(25,31,30,27)(28,34,37,39)(33,38,36,35);(24,27,29,31)(25,32,30,26)(28,35,37,38)(33,39,36,34);(16,18,19,22)(17,21,20,23)(24,28,29,37)(25,33,30,36)(26,34,32,39)(27,35,31,38)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27225);