Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60454 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27×C4 |
| direct product | C11×#60621 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3449 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G | |
2078 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
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)(22,30)(23,25)(24,28)(26,29)(27,31)(32,34)(33,35);(13,16)(17,19)(20,22,25,33,26,32,24,31)(21,27,28,34,29,35,23,30);(12,14,15,18)(13,17,16,19)(20,23,24,29,26,28,25,21)(22,30,31,35,32,34,33,27);(20,24,26,25)(21,28,29,23)(22,31,32,33)(27,34,35,30);(22,32)(27,35)(30,34)(31,33)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53609);