Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23427 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#135 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G | |
1986 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)(22,29)(23,31)(24,27)(25,34)(26,28)(30,33)(32,35);(13,15)(16,17)(18,19)(20,22,26,32)(21,23,28,33)(24,31,25,30)(27,35,34,29);(17,19)(20,23)(21,22)(24,29)(25,35)(26,33)(27,30)(28,32)(31,34);(20,24,26,25)(21,27,28,34)(22,30,32,31)(23,29,33,35)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16415);