Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23590 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×#120 |
| prime radical | C11×#537 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G | |
1074 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21)(22,26)(23,31)(24,33)(25,29)(27,32)(28,34)(30,35);(13,16)(17,19)(20,22,25,23)(21,26,29,31)(24,32,34,30)(27,28,35,33);(20,23,25,22)(21,27,29,35)(24,30,34,32)(26,33,31,28);(12,14,15,18)(13,17,16,19)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16578);