Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1426 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#7464 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #367 |
| commutator | C16 | C2×C8×C11 |
| Frattini, cosocle | C4×C16 | C22×C11 |
| socle | C2×C11 | #1372 |
| prime radical | C22×C11 | #368 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C2×C8×C11 ◁ C4×C8×C11 ◁ C4×C11×C16 ◁ G | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 2 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,22,18,23,39,49,19,25,34,53,41,24,17,40)(14,26,29,55,31,57,30,67,32,59,38,56,68,58,69,75)(15,33,27,50,36,70,60,52,37,71,61,51,66,43,35,21)(20,42,44,73,46,74,72,28,48,62,45,64,47,63,54,65);(12,14,27,42,17,30,15,28,41,68,35,63,34,29,66,73,19,32,61,62,39,69,37,65,18,31,60,74,16,38,36,64)(13,20,43,67,22,45,21,26,23,46,33,56,49,54,50,57,25,48,70,75,53,44,52,59,24,47,71,55,40,72,51,58)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 452);