Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2121 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#11474 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#99 |
| commutator | C23 | C22×C8×C11 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C11 |
| prime radical | C22×D4×C11 | C2×C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×D4×C11 ◁ G | |
460 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)(12,13,15,18,16,19,14,17)(20,21)(22,28)(23,31,32,26)(24,27)(25,30,33,35)(29,34);(20,22,24,29)(21,25,27,33)(23,30,32,35)(26,28,31,34);(12,14,16,15)(13,17,19,18)(22,29)(25,33)(28,34)(30,35)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4462);