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×#33381 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C2×C11×#576 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#41 ◁ C2×C11×#131 ◁ G | |
1176 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
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)(16,17)(18,23)(19,22)(20,33)(21,26)(24,30)(25,31)(27,37)(28,34)(29,43)(32,36)(35,44)(38,42)(39,41)(40,45)(46,47);(17,22)(19,30)(20,31)(23,34)(24,25)(26,36)(28,42)(29,41)(32,44)(33,35)(37,45)(38,39)(40,47)(43,46);(16,18)(17,23)(19,28)(20,29)(21,27)(22,34)(24,38)(25,39)(26,37)(30,42)(31,41)(32,40)(33,43)(35,46)(36,45)(44,47);(18,27)(23,37)(28,40)(29,41)(34,45)(38,46)(39,43)(42,47)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26369);