Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C27×C4 |
| direct product | C11×#60125 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C22×C11 | C24×C4 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ G | |
2122 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)(14,17)(15,16)(18,19)(20,21,23,27,24,26,30,33)(22,25,29,32,28,31,34,35);(13,16)(17,19)(20,22)(21,25)(23,29)(24,28)(26,31)(27,32)(30,34)(33,35);(12,14,15,18)(13,17,16,19)(20,22)(21,25)(23,29)(24,28)(26,31)(27,32)(30,34)(33,35);(22,28)(25,31)(29,34)(32,35);(21,26)(25,31)(27,33)(32,35)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53113);