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×#11013 |
| 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 | |
1262 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)(18,26,29,22)(19,23)(20,25)(21,24)(27,44,45,36)(28,42,33,37)(30,47,46,38)(31,40)(32,39)(34,43)(35,41);(16,18)(17,22)(19,30)(20,33)(21,29)(23,38)(24,26)(25,42)(27,31)(28,35)(32,46)(34,45)(36,40)(37,41)(39,47)(43,44);(13,15)(16,19,21,32)(17,23,24,39)(18,27,29,45)(20,34,35,31)(22,36,26,44)(25,43,41,40)(28,46,33,30)(37,47,42,38)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4001);