Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2230 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#13186 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #476 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C23×C11 | AGL(1,ℤ/8) |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
310 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(17,23,26,24)(18,27)(19,28)(20,21)(25,31,30,29);(16,17,21,30,22,26,20,25)(18,24,19,29,28,23,27,31);(12,13,14,15)(16,18,20,27,22,28,21,19)(17,24,25,31,26,23,30,29)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6174);