Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24468 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24470 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3489 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1360 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)(16,17,22,27,23,28,21,37)(18,29,20,24,31,26,36,40)(19,32,34,43,35,42,38,25)(30,45,46,41,47,39,33,44);(12,13)(14,15)(16,18)(17,24)(19,30)(20,22)(21,36)(23,31)(25,39)(26,27)(28,40)(29,37)(32,44)(33,38)(34,46)(35,47)(41,42)(43,45);(13,15)(16,19,23,35)(17,25,28,43)(18,30,31,47)(20,33,36,46)(21,34,22,38)(24,39,40,45)(26,41,29,44)(27,42,37,32);(16,20)(17,26)(18,21)(19,33)(22,31)(23,36)(24,37)(25,41)(27,40)(28,29)(30,34)(32,39)(35,46)(38,47)(42,45)(43,44)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17458);