Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#10656 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | #121 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
334 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,19)(15,17)(16,18)(20,21,24,25,23,27,22,26)(29,32)(33,35);(12,14,16,15)(13,17,18,19)(20,22,23,24)(21,25,27,26)(29,33)(31,34)(32,35);(12,15,16,14)(13,17,18,19)(21,26)(22,24)(25,27)(28,29)(30,32)(31,35)(33,34)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3644);