Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9103 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11074 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
866 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,21,27,22,26,20,25)(18,23,29,37,30,38,35,42)(19,31,33,24,34,41,32,40)(28,43,44,39,45,47,46,36);(12,13,14,15)(16,18)(17,23)(19,28)(20,35)(21,29)(22,30)(24,39)(25,42)(26,38)(27,37)(31,43)(32,46)(33,44)(34,45)(36,40)(41,47);(16,19,22,34)(17,24,26,40)(18,28,30,45)(20,33,21,32)(23,36,38,39)(25,41,27,31)(29,46,35,44)(37,47,42,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4062);