Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23906 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24313 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
998 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)(12,13,16,19)(14,18,15,17)(20,21)(22,25)(23,26)(24,28)(27,32)(29,33)(30,35)(31,34);(12,14,16,15)(13,17,19,18)(20,22,24,30)(21,25,28,35)(23,31,32,29)(26,34,27,33);(21,26)(23,32)(25,33)(27,28)(29,31)(34,35);(12,15,16,14)(13,18,19,17)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17301);