Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#23147 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C11×#3050 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C11×C22⋊C8 ◁ G | |
808 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(17,19)(20,21,24,29,25,30,34,28)(22,26,23,32,31,27,33,35);(12,13)(14,17)(15,16)(18,19)(20,22,24,23,25,31,34,33)(21,26,29,32,30,27,28,35);(12,14,15,18)(13,17,16,19)(20,23,24,31,25,33,34,22)(21,27,28,32,30,26,29,35);(13,16)(17,19)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16135);