Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#20986 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C24 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×Q8×C11 ◁ G | |
1718 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)(18,22,28,35)(19,23)(20,24)(21,25)(26,33,41,45)(27,34,43,47)(29,36)(30,37)(31,38)(32,39)(40,44,42,46);(16,18)(17,22,25,35)(19,26)(20,27)(21,28)(23,33,37,45)(24,34,39,47)(29,40)(30,41)(31,42)(32,43)(36,44,38,46);(13,15)(16,19,21,30)(17,23,25,37)(18,26,28,41)(20,31,32,29)(22,33,35,45)(24,38,39,36)(27,42,43,40)(34,46,47,44);(16,20,21,32)(17,24,25,39)(18,27,28,43)(19,29,30,31)(22,34,35,47)(23,36,37,38)(26,40,41,42)(33,44,45,46)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13974);