Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23609 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C23×C11 | C22×D4 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C22×C42×C11 ◁ G | |
1138 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(20,21)(22,31)(23,32)(24,28)(25,29)(26,30)(27,34)(33,35);(16,17)(18,19)(20,22,24,32,26,27,25,33)(21,23,29,31,30,35,28,34);(13,15)(17,19)(20,23)(21,27)(22,30)(24,34)(25,31)(26,35)(28,33)(29,32);(20,24,26,25)(21,28,30,29)(22,32,27,33)(23,34,35,31)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16597);