Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33480 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C11×C16 | C23 |
| 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×C11×C16 ◁ G | |
526 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)(22,26,30,37,31,38,42,48,32,36,43,46,44,47,50,51);(13,16)(17,19);(20,22,23,30,24,31,33,42,25,32,34,43,35,44,45,50)(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)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26468);