Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#10999 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #379 |
| prime radical | C11×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
1310 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)(16,17,21,25,22,26,20,33)(18,27,29,23,30,38,34,37)(19,24,31,40,32,41,35,39)(28,43,46,47,45,42,44,36);(12,13)(14,15)(16,18)(17,23)(19,28)(20,34)(21,29)(22,30)(24,36)(25,38)(26,37)(27,33)(31,46)(32,45)(35,44)(39,42)(40,43)(41,47);(13,15)(16,19)(17,24)(18,28)(20,35)(21,31)(22,32)(23,36)(25,40)(26,41)(27,42)(29,46)(30,45)(33,39)(34,44)(37,47)(38,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3987);