Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C29 |
| direct product | C2×C4×C11×#137 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C2×D4 |
| commutator | C4 | C24×C4×C11 |
| Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C23×C11 | C22×D4 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C22×C42×C11 ◁ G | |
2810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33);(3,4,5,6);(7,8)(9,15)(10,18)(11,13)(12,16)(14,20)(17,22)(19,21);(7,9,11,17)(8,12,13,21)(10,19,20,16)(14,22,18,15);(8,13)(12,21)(14,18)(15,22)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53145);