Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C11 · Schur multiplier (H2) = C42 |
| direct product | C11×#8138 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C42 |
| commutator | C4 | C2×C4×C8×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | #376 |
| prime radical | C23×C11 | #117 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ G | |
354 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,17,14,16,18,19)(20,21)(22,30,33,43)(23,27)(24,28)(25,29)(26,32,38,46)(31,42,45,50)(34,39)(35,40)(36,41)(37,44,48,51)(47,49);(13,16)(17,19)(20,22)(21,26,29,38)(23,31)(24,32)(25,33)(27,37,40,48)(28,30,41,43)(34,44)(35,45)(36,46)(39,42,49,50)(47,51);(20,23,24,34,25,35,36,47)(21,27,28,39,29,40,41,49)(22,31,32,44,33,45,46,51)(26,37,30,42,38,48,43,50)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1126);