Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8603 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#11098 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #117 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #380 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C22×C11×M16 ◁ G | |
882 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)(16,17)(18,26)(19,30,32,23)(20,33)(21,25)(22,28)(24,34)(27,40,42,38)(29,39)(31,37,46,45)(35,41,44,47)(36,43);(12,13)(14,15)(16,18,20,28,21,29,34,43)(17,22,24,26,25,36,33,39)(19,27,31,41,32,42,46,47)(23,35,37,38,30,44,45,40);(13,15)(16,19)(17,23)(18,27)(20,31)(21,32)(22,35)(24,37)(25,30)(26,38)(28,41)(29,42)(33,45)(34,46)(36,44)(39,40)(43,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4086);