Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11×C16 · Schur multiplier (H2) = C22 |
| direct product | C11×SD16⋊C16 |
| unambiguous semidirect product | SD16⋊(C11×C16) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C2×D4 |
| commutator | C4 | C22×C11×C16 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C22×C11 | C8×D4 |
| prime radical | C2×D4×C11 | C2×C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ C4×C11×C16 ◁ G | |
232 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,16)(15,17)(18,19)(20,21,23,27,24,28,31,34,25,22,26,29,32,30,33,35);(13,16)(14,19)(17,18);(13,17)(16,18)(20,22,23,29,24,30,31,35,25,21,26,27,32,28,33,34)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5043);