Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24278 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24282 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1308 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)(16,17,23,29)(18,30,20,38)(19,34,37,43)(21,28,22,27)(24,33,26,32)(25,39,42,36)(31,41,35,40)(44,46,47,45);(12,13)(14,15)(16,18,22,33,23,20,21,32)(17,24,28,38,29,26,27,30)(19,31,39,46,37,35,36,45)(25,40,43,47,42,41,34,44);(13,15)(16,19)(17,25)(18,31)(20,35)(21,36)(22,39)(23,37)(24,40)(26,41)(27,34)(28,43)(29,42)(30,44)(32,45)(33,46)(38,47);(16,20,22,32,23,18,21,33)(17,26,28,30,29,24,27,38)(19,35,39,45,37,31,36,46)(25,41,43,44,42,40,34,47)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17270);