Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23903 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24114 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C11 |
| prime radical | C11×#3490 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C25×C11 ◁ G | |
1254 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,19)(15,17)(16,18)(20,21)(22,25)(23,26)(24,27)(28,33)(29,32)(30,34)(31,35);(12,14,16,15)(13,17,18,19)(20,22)(21,25)(23,28)(24,29)(26,33)(27,32)(30,35)(31,34);(12,15,16,14)(13,17,18,19)(20,23)(21,26)(22,28)(24,30)(25,31)(27,34)(29,35)(32,33);(13,18)(17,19)(23,30)(26,34)(28,35)(31,33)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17102);