Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3003 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#21070 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C8×C11 ◁ G | |
1026 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,14)(16,17,21,26,22,25,20,34)(18,23,29,38,30,37,28,44)(19,31,32,24,33,40,35,39)(27,41,42,36,43,47,45,46);(12,13,15,14)(16,18,21,29,22,30,20,28)(17,23,26,38,25,37,34,44)(19,27,32,42,33,43,35,45)(24,36,40,47,39,46,31,41);(12,14,15,13)(16,19)(17,24)(18,27)(20,35)(21,32)(22,33)(23,36)(25,39)(26,40)(28,45)(29,42)(30,43)(31,34)(37,46)(38,47)(41,44);(17,25)(23,37)(24,39)(26,34)(31,40)(36,46)(38,44)(41,47)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14058);