Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11104 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #121 |
| 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 ◁ C23×C4×C11 ◁ G | |
866 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)(18,27)(19,32,34,39)(20,35)(21,25)(22,26)(23,29)(24,33,40,36)(28,37,44,47)(30,38)(31,42)(41,43,46,45);(12,13)(14,15)(16,18,20,29,22,31,21,30)(17,23,25,27,26,38,35,42)(19,28,33,43,34,44,36,45)(24,37,39,41,40,47,32,46);(13,15)(16,19)(17,24)(18,28)(20,33)(21,36)(22,34)(23,37)(25,39)(26,40)(27,41)(29,43)(30,45)(31,44)(32,35)(38,47)(42,46)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4092);