Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2190 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13025 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #447 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#97 ◁ G | |
522 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,20,25,23,30,31,28,22,26,19,24,21,18,27,29);(12,13,14,15)(16,18,22,30)(17,23,26,21)(19,25,20,24)(27,29,31,28);(16,17)(18,23)(19,29)(20,28)(21,30)(22,26)(24,27)(25,31)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6013);