Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10500 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#10502 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C11×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
412 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,18)(14,19)(15,16)(20,21)(22,26)(23,25)(24,28)(27,31)(29,32)(30,33)(34,35);(12,13,17,19)(14,16,18,15)(21,25)(22,29)(23,31)(26,33)(27,28)(30,35);(12,14,15,13,17,18,16,19)(20,22,23,29,24,30,31,35)(21,26,27,34,28,33,25,32)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3490);