Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33481 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C24 |
| commutator | C22 | C23×C8×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C22×C11 | C23×C8 |
| prime radical | C11×#121 | C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ G | |
508 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21,23,28,24,29,33,41,25,27,34,39,35,40,45,49)(22,26,31,37,32,38,44,48,30,36,42,46,43,47,50,51);(13,16)(17,19)(22,30)(26,36)(31,42)(32,43)(37,46)(38,47)(44,50)(48,51);(20,22,23,31,24,32,33,44,25,30,34,42,35,43,45,50)(21,26,28,37,29,38,41,48,27,36,39,46,40,47,49,51);(12,14,15,18)(13,17,16,19)(21,27)(26,36)(28,39)(29,40)(37,46)(38,47)(41,49)(48,51)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26469);