Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8325 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11388 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #379 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
878 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)(20,21)(22,29,31,26)(23,25)(24,28)(27,32)(30,34,35,33);(12,13,15,17)(14,18,19,16)(21,25)(23,32)(26,33)(27,28)(29,34)(30,35);(12,14,15,19)(13,16,17,18)(20,22)(21,26)(23,30)(24,31)(25,33)(27,34)(28,29)(32,35)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4376);