Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#10357 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
452 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)(12,13,15,17)(14,18,19,16)(21,24)(22,26)(25,27)(28,29,30,33)(31,32,35,34);(12,14,15,19)(13,16,17,18)(28,29)(30,33)(31,32)(34,35);(20,21,23,25)(22,27,26,24)(29,32)(31,35)(33,34)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3345);