Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12077 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13039 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #442 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#97 ◁ G | |
472 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)(16,17,22,28,32,47,20,39,24,30,21,41,23,29,40,27)(18,31,33,45,42,26,38,44,35,46,37,25,34,43,19,36);(12,13,14,15)(16,18,32,34,24,35,23,42)(17,25,29,36,30,45,47,44)(19,20,37,21,38,40,33,22)(26,28,46,27,43,41,31,39);(16,19)(17,26)(18,20)(21,34)(22,42)(23,33)(24,38)(25,28)(27,36)(29,46)(30,43)(31,47)(32,37)(35,40)(39,44)(41,45)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6027);