Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12019 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#12887 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#106 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C23×C11 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
286 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)(14,17)(15,16)(18,19)(20,21)(22,32,36,47)(23,38,37,51)(24,40)(25,41)(26,31)(27,35,45,48)(28,39,46,49)(29,34)(30,42)(33,44)(43,50);(13,16)(17,19)(20,22,33,48,25,37,50,39,26,36,24,35,42,23,34,49)(21,27,43,47,30,28,44,51,31,45,29,32,41,46,40,38);(12,14,15,18)(13,17,16,19)(20,23,24,39,25,22,34,35,26,37,33,49,42,36,50,48)(21,28,29,38,30,45,40,47,31,46,43,51,41,27,44,32)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5875);