Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7035 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#7050 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | #95 |
| commutator | C22×C4 | C42×C11 |
| Frattini, cosocle | C43 | C22×C11 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C43×C11 ◁ G | |
332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17)(14,15)(18,19)(20,21)(22,24)(23,26)(25,27)(28,29,30,33,31,32,34,35);(12,13,15,18,16,19,14,17)(21,24)(22,27)(25,26)(29,32)(30,34)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 38);