Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13329 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C22×C11×D8 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
578 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(20,21,25,30)(22,31,34,49)(23,27,38,45)(24,39,37,29)(26,41,43,32)(28,46,44,36)(33,50,40,47)(35,48,51,42);(13,15)(16,17)(18,19)(20,22,25,34)(21,26,30,43)(23,35,38,51)(24,40,37,33)(27,31,45,49)(28,47,44,50)(29,48,39,42)(32,46,41,36);(17,19)(21,27)(23,36)(24,37)(26,31)(28,29)(30,45)(32,35)(33,40)(38,46)(39,44)(41,51)(42,50)(43,49)(47,48)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6317);