Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1468 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#10914 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | C4×C22⋊C4 |
| prime radical | C24×C11 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C8×C11 ◁ G | |
698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,20,24,21,25,32,38)(18,26,29,40,28,22,33,35)(19,23,30,36,31,37,43,46)(27,39,42,47,41,34,44,45);(16,18)(17,22,25,26)(19,27)(20,29)(21,28)(23,34,37,39)(24,35,38,40)(30,42)(31,41)(32,33)(36,45,46,47)(43,44);(13,15)(16,19,20,30,21,31,32,43)(17,23,24,36,25,37,38,46)(18,27,29,42,28,41,33,44)(22,34,35,45,26,39,40,47)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3902);