Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2238 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#13139 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #481 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C23×C11 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#97 ◁ G | |
318 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,14)(16,17)(18,26,29,42)(19,22)(20,32)(21,35)(23,28,37,44)(24,34)(25,27)(30,45,36,40)(31,46)(33,39,47,41)(38,43);(12,13,15,14)(17,22)(20,31)(23,37)(25,35)(28,44)(33,47)(34,43)(39,41);(12,14,15,13)(16,18,27,30,19,29,21,36)(17,23,35,39,22,37,25,41)(20,33,43,44,31,47,34,28)(24,40,46,42,38,45,32,26)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6127);