Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13068 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13068 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #1893 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C2×C11×#131 ◁ G | |
470 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)(14,23)(15,28,31,39)(16,26)(17,21)(18,25)(19,22)(20,30,38,36)(24,29,37,32)(27,33)(34,35)(40,41,43,42);(12,14,23,13,18,26,34,21,19,27,33,22,17,35,16,25)(15,24,40,20,30,42,29,39,31,37,43,38,36,41,32,28);(12,15)(13,20)(14,24)(16,32)(17,36)(18,30)(19,31)(21,39)(22,38)(23,40)(25,28)(26,42)(27,37)(29,34)(33,43)(35,41)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6056);