Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11368 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #124 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #400 |
| prime radical | C24×C11 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
574 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)(12,13)(14,15)(16,17,22,25,21,26,20,35)(18,27,29,23,30,39,36,38)(19,24,32,42,33,43,34,41)(28,40,31,37,46,44,45,47);(13,15)(16,18,22,29,21,30,20,36)(17,23,25,39,26,38,35,27)(19,31,34,28,33,45,32,46)(24,40,41,47,43,44,42,37);(13,15)(16,19,22,34,21,33,20,32)(17,24,25,41,26,43,35,42)(18,28,29,45,30,46,36,31)(23,37,39,40,38,47,27,44)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4356);