Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #58990 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C26×C4 |
| direct product | C11×#59947 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2334 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)(12,13)(14,15)(16,17)(18,19)(20,21,25,26)(22,24,23,27)(29,32)(33,35);(13,17)(14,18)(21,26)(22,23)(28,29)(30,33)(31,32)(34,35);(20,22,25,23)(21,27,26,24)(28,30,31,34)(29,33,32,35);(12,14,16,18)(13,15,17,19)(20,23,25,22)(21,24,26,27);(12,15)(13,18)(14,17)(16,19)(20,24)(21,22)(23,26)(25,27)(28,29)(30,33)(31,32)(34,35)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 52935);