Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17411 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#17411 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#546 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C11×#41 ◁ G | |
1424 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18,19,16)(15,17)(20,21,23,26,24,27,30,33)(22,25,29,32,28,31,34,35);(12,14)(13,16)(15,19)(17,18);(20,22)(21,25)(23,29)(24,28)(26,32)(27,31)(30,34)(33,35);(22,28)(25,31)(29,34)(32,35)605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 10399);