Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32941 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#32943 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1316 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)(16,17,22,27)(18,28,32,38)(19,33,35,41)(20,26,21,25)(23,31,39,30)(24,36,40,34)(29,43,45,37)(42,46,47,44);(16,18,21,31,22,32,20,30)(17,23,26,38,27,39,25,28)(19,29,36,46,35,45,34,44)(24,37,41,47,40,43,33,42);(16,19)(17,24)(18,29)(20,34)(21,36)(22,35)(23,37)(25,33)(26,41)(27,40)(28,42)(30,44)(31,46)(32,45)(38,47)(39,43);(13,15)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25931);