Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#8811 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C2×D4 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle, prime radical | C23×C11 | C2×C4⋊C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C43×C11 ◁ G | |
362 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17)(18,24)(19,27)(20,22)(21,25)(23,28)(26,30)(29,31)(32,33,35,38,36,39,42,45)(34,37,41,44,40,43,46,47);(16,18,19,25,20,26,28,31)(17,21,23,24,22,29,27,30)(32,34)(33,37)(35,41)(36,40)(38,44)(39,43)(42,46)(45,47);(12,13,14,15)(17,22)(21,29)(23,27)(24,30)(34,40)(37,43)(41,46)(44,47)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1799);