Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2104 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11318 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #401 |
| commutator | C24 | C22×C4×C11 |
| Frattini, cosocle | C25 | C23×C11 |
| prime radical | C25×C11 | C23 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C25×C11 ◁ G | |
782 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,21,25,29)(19,26)(20,23)(22,27)(24,28,31,30);(12,13)(14,15)(16,18)(17,21,23,29)(19,24,27,31)(20,25)(22,30)(26,28);(13,15)(16,19)(17,22,23,26)(18,24,25,31)(20,27)(21,28)(29,30)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4306);