Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#12008 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C11 | D8 |
| commutator | C8 | C22×C8×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C22×C11 | C2×#107 |
| prime radical | C23×C11 | #107 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
242 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)(12,13,14,16,15,17,18,19)(20,21)(22,31)(23,28)(24,38)(25,40)(26,30)(27,34)(29,32)(33,44)(35,50)(36,46)(37,43)(39,51)(41,48)(42,49)(45,47);(20,22,32,47,25,35,39,49,26,36,37,48,23,33,24,34)(21,27,38,44,28,41,43,46,30,42,51,50,40,45,29,31);(20,23,26,25)(21,28,30,40)(22,33,36,35)(24,37,39,32)(27,41,42,45)(29,38,43,51)(31,44,46,50)(34,48,49,47)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4996);