Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #58990 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#60011 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1670 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,14)(15,18,19,17)(20,21)(22,23)(24,26)(25,27)(28,29,32,31)(30,34,35,33);(13,14)(17,18)(20,22,24,27)(21,23,26,25)(28,30)(29,33)(31,34)(32,35);(20,21,24,26)(22,25,27,23)(28,31,32,29)(30,34,35,33);(12,14,16,13)(15,18,19,17)(20,22)(21,25)(23,26)(24,27);(12,15)(13,17)(14,18)(16,19)(20,23,24,25)(21,22,26,27)(28,30)(29,33)(31,34)(32,35)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 52999);