Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2069 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11140 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #396 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
822 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)(13,15)(16,17,21,25,22,26,20,37)(18,27,31,39,30,43,29,23)(19,32,35,41,36,24,34,40)(28,44,46,47,33,42,45,38);(12,13,14,15)(16,18,20,29,22,30,21,31)(17,23,25,27,26,39,37,43)(19,33,34,46,36,28,35,45)(24,38,40,44,32,47,41,42);(16,19,22,36)(17,24,26,32)(18,28,30,33)(20,35,21,34)(23,38,39,47)(25,41,37,40)(27,42,43,44)(29,46,31,45)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4128);