Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2021 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11088 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator | C24 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #385 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ 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)(12,13)(14,15)(16,17,20,25,21,24,32,38)(18,22,28,34,27,35,40,45)(19,23,31,37,30,36,43,46)(26,33,39,44,29,41,42,47);(16,18)(17,22)(19,29,30,26)(20,28)(21,27)(23,33,36,41)(24,35)(25,34)(31,42,43,39)(32,40)(37,44,46,47)(38,45);(13,15)(16,19)(17,23)(18,26)(20,31)(21,30)(22,33)(24,36)(25,37)(27,29)(28,39)(32,43)(34,44)(35,41)(38,46)(40,42)(45,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4076);