Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#8258 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | C4×C22⋊C4 |
| prime radical | C23×C11 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
406 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,18)(17,19)(20,21,24,29,25,30,33,28)(22,23,27,34,32,35,31,26);(12,14,16,19,17,18,15,13)(20,22,24,27,25,32,33,31)(21,26,29,23,30,34,28,35);(12,15,17,16)(13,14,19,18)(20,23,33,26,25,35,24,34)(21,27,28,22,30,31,29,32)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1246);