Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9091 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#11015 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1242 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)(12,13)(14,15)(16,17,21,27,22,25,20,26)(18,28,31,38,32,23,30,39)(19,24,34,42,35,41,36,43)(29,44,33,47,45,37,46,40);(16,18,22,32)(17,23,25,28)(19,33,35,46)(20,31,21,30)(24,40,41,47)(26,39,27,38)(29,36,45,34)(37,43,44,42);(13,15)(16,19)(17,24)(18,29)(20,36)(21,34)(22,35)(23,37)(25,41)(26,43)(27,42)(28,44)(30,46)(31,33)(32,45)(38,47)(39,40)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4003);