Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27×C4 |
| direct product | C11×#60623 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G | |
2042 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21,26,28)(22,29,23,25)(24,27,32,34)(30,35,31,33);(13,16)(17,19)(20,22,25,21,26,23,29,28)(24,30,33,27,32,31,35,34);(12,14,15,18)(13,17,16,19)(20,23,25,28,26,22,29,21)(24,31,33,34,32,30,35,27);(20,24)(21,27)(22,30)(23,31)(25,33)(26,32)(28,34)(29,35);(24,32)(27,34)(30,31)(33,35)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53611);