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) = C22×C4 |
| direct product | C11×#7916 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G | |
622 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,24,26,21)(19,22)(20,23)(25,30,31,28)(27,29)(32,33,35,39,36,38,44,46)(34,40,42,47,41,37,43,45);(12,13,14,15)(16,18)(17,21)(19,25)(20,26)(22,28)(23,24)(27,31)(29,30)(32,34)(33,37)(35,43)(36,41)(38,40)(39,47)(42,44)(45,46);(16,19,20,27)(17,22,23,29)(18,25,26,31)(21,28,24,30)(34,41)(37,40)(42,43)(45,47)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 904);