Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#10476 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #121 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C22×D4×C11 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
506 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,20)(19,22)(21,23)(24,25,28,30)(26,31,29,27);(12,13)(14,15)(25,26)(27,31)(29,30);(13,15)(17,20)(18,23)(21,22)(24,26,27,25,28,29,31,30)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3464);