Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#13182 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #459 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C2×C11 | #1947 |
| prime radical | C23×C11 | #137 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
280 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,18,23,19,24,17,34)(14,25,28,41,29,35,27,39)(15,22,16,32,31,40,30,21)(20,33,36,43,38,42,37,26);(12,14,18,28,19,29,17,27)(13,20,23,36,24,38,34,37)(15,26,16,33,31,43,30,42)(21,35,22,39,32,25,40,41);(12,15,17,30,19,31,18,16)(13,21,23,22,24,32,34,40)(14,26,27,42,29,43,28,33)(20,35,36,39,38,25,37,41)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6170);