Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #36702 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#36816 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C11×#2404 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1800 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(14,18)(17,19)(21,25)(23,27)(28,29,33,36)(30,37,31,34)(32,40,41,35)(38,42,39,43);(13,16)(17,19)(21,25)(22,26)(28,30,33,31)(29,34,36,37)(32,38,41,39)(35,42,40,43);(12,13)(14,17)(15,16)(18,19)(20,21,24,25)(22,23,26,27)(28,31,33,30)(29,34,36,37)(32,39,41,38)(35,42,40,43);(12,13)(14,17)(15,16)(18,19)(20,22,24,26)(21,23,25,27)(28,29)(30,37)(31,34)(32,35)(33,36)(38,43)(39,42)(40,41);(12,14)(13,17)(15,18)(16,19)(20,23)(21,26)(22,25)(24,27)(28,32,33,41)(29,35,36,40)(30,38,31,39)(34,42,37,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29804);