Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#18516 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| socle | C22×C11 | C2×#120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G | |
1258 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)(14,16)(15,18)(17,19)(20,21)(22,31)(23,28)(24,29)(25,30)(26,33)(27,32)(34,35);(13,16)(14,19)(17,18)(20,22)(21,26)(23,32)(24,33)(25,34)(27,30)(28,31)(29,35);(20,22)(21,27)(23,32)(24,33)(25,34)(26,30)(28,35)(29,31);(20,23,25,24)(21,28,30,29)(22,32,34,33)(26,31,27,35)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11504);