Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #22284 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#22286 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2328 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3155 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
820 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,26,30,24)(16,31)(18,22)(19,23)(20,29,36,28)(21,32)(25,34)(27,40,43,35)(33,37)(38,41,39,42);(12,14,18,23,19,22,17,13)(15,20,28,26,30,36,29,24)(16,25,33,37,34,31,32,21)(27,35,41,39,43,40,42,38);(12,15)(13,20,23,36)(14,24,22,26)(16,27)(17,28)(18,29)(19,30)(21,35,37,40)(25,38,31,39)(32,41)(33,42)(34,43);(12,16,18,33,19,34,17,32)(13,21,14,25,23,37,22,31)(15,27,29,42,30,43,28,41)(20,35,24,38,36,40,26,39)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15274);