Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1909 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#10947 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
914 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)(18,26,29,22)(19,30)(20,33)(21,24)(23,32)(25,35)(27,41,42,47)(28,37,34,39)(31,44)(36,43,40,46)(38,45);(12,13,14,15)(16,18)(17,22)(19,27)(20,34)(21,29)(23,36)(24,26)(25,39)(28,35)(30,41)(31,42)(32,46)(33,37)(38,40)(43,45)(44,47);(16,19,20,32,21,31,35,45)(17,23,25,30,24,38,33,44)(18,27,34,46,29,42,28,43)(22,36,39,41,26,40,37,47)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3935);