Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #36702 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C26×C4 |
| direct product | C11×#36818 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2056 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)(14,18)(22,26)(25,27)(29,33)(30,31);(12,13,16,15)(14,19,18,17)(21,24)(25,27)(28,29,32,33)(30,34,31,35);(20,21)(22,25)(23,24)(26,27)(28,30,32,31)(29,34,33,35);(12,14,16,18)(13,17,15,19)(20,21)(22,25)(23,24)(26,27)(28,29)(30,34)(31,35)(32,33);(12,15,16,13)(14,19,18,17)(20,22)(21,25)(23,26)(24,27)(28,31,32,30)(29,35,33,34)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29806);