Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#22973 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G | |
758 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17)(18,21)(19,20)(22,23)(24,25)(26,33)(27,31)(28,36)(29,32)(30,35)(34,39)(37,38);(12,14,15,13)(17,20)(18,22)(26,34)(30,38)(33,39)(35,37);(24,26,29,34)(25,30,32,38)(27,35,28,37)(31,39,36,33);(16,18,19,22)(17,21,20,23)(24,27,29,28)(25,31,32,36)(26,35,34,37)(30,39,38,33)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15961);