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×#59992 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2174 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(17,18)(20,21)(22,24)(23,26)(25,27)(30,34)(31,35);(12,13,16,15)(14,18,19,17)(21,22)(25,26)(28,29,33,32)(30,35,34,31);(20,21,24,22)(23,25,27,26)(28,30)(29,31)(32,35)(33,34);(12,14,16,19)(13,17,15,18)(20,22,24,21)(23,26,27,25)(28,31,33,35)(29,34,32,30);(12,15,16,13)(14,18,19,17)(20,23)(21,25)(22,26)(24,27)(28,32,33,29)(30,35,34,31)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 52980);