Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #3415 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33382 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C2×C11×#578 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#41 ◁ C2×C11×#131 ◁ G | |
1124 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(17,22)(19,29)(20,31)(23,35)(24,39)(25,36)(27,42)(28,41)(30,33)(32,34)(37,46)(38,47)(40,45)(43,44);(16,17,21,25)(18,23,26,37)(19,30,32,39)(20,33,31,24)(22,34,36,29)(27,43,40,47)(28,44,41,38)(35,45,46,42);(16,18)(17,23)(19,27)(20,28)(21,26)(22,35)(24,38)(25,37)(29,42)(30,43)(31,41)(32,40)(33,44)(34,45)(36,46)(39,47);(18,26)(23,37)(27,40)(28,41)(35,46)(38,44)(42,45)(43,47)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26370);