Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C27×C4 |
| direct product | C11×#34346 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| socle | C23×C11 | C25 |
| prime radical | C2×C11×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
2442 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)(16,17)(18,22)(19,21)(20,23)(24,25)(26,32)(27,31)(28,30)(29,33)(34,38)(35,37)(36,39);(18,23)(20,22)(24,26)(25,29)(27,34)(28,33)(30,32)(31,36)(35,39)(37,38);(16,18,19,23)(17,20,21,22)(26,33)(29,32)(34,39)(36,38);(17,21)(20,22)(25,30)(26,33)(31,37)(34,39);(24,27,28,35)(25,31,30,37)(26,34,33,39)(29,36,32,38)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27334);