Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24404 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#25566 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C11 |
| prime radical | C11×#534 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1122 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)(14,18)(15,17)(16,19)(20,21)(22,26)(23,27)(24,28)(25,29)(30,31)(32,35)(33,34);(12,14,15,19)(13,16,17,18)(20,22)(21,26)(23,33)(24,31)(25,32)(27,34)(28,30)(29,35);(20,23,25,28)(21,27,29,24)(22,30)(26,34)(31,35)(32,33);(13,17)(16,18)(20,24,25,27)(21,28,29,23)(22,31,32,34)(26,30,35,33)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 18554);