Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18371 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3493 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
924 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(14,18)(17,19)(20,21,25,29)(22,26,32,39)(23,27,34,41)(24,35,36,28)(30,42,44,37)(31,45,46,38)(33,47,48,40)(43,49,51,50);(12,13)(14,19)(15,17)(16,18)(20,22)(21,26)(23,30)(24,31)(25,32)(27,37)(28,38)(29,39)(33,43)(34,44)(35,45)(36,46)(40,49)(41,42)(47,50)(48,51);(20,23,25,34)(21,27,29,41)(22,30,32,44)(24,33,36,48)(26,37,39,42)(28,40,35,47)(31,43,46,51)(38,49,45,50);(13,17)(16,19)(20,24,25,36)(21,28,29,35)(22,31,32,46)(23,33,34,48)(26,38,39,45)(27,40,41,47)(30,43,44,51)(37,49,42,50)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11359);