Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11858 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#11987 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#102 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| prime radical | C23×C11 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
300 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)(13,17)(14,15)(18,19)(20,21,24,30,38,46,39,48,26,28,23,29,25,31,41,50)(22,32,34,45,42,49,37,27,36,44,33,51,35,47,40,43);(12,13)(14,17)(15,19)(16,18)(20,22,26,36)(21,27,28,43)(23,37,24,40)(25,42,38,35)(29,47,30,49)(31,51,46,45)(32,50,44,48)(33,41,34,39);(12,14,16,15)(13,17,18,19)(21,28)(27,43)(29,30)(31,46)(32,44)(45,51)(47,49)(48,50)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4975);