Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#22896 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D42 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×H(5,𝔽2) | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G | |
1016 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17)(18,29)(19,25)(20,27)(21,26)(22,28)(23,32)(24,34)(30,38)(31,45)(33,44)(35,43)(36,40)(37,41)(39,47)(42,46);(12,14,15,13)(16,18)(17,23)(19,30)(20,36)(21,32)(22,33)(24,38)(25,42)(26,44)(27,29)(28,40)(31,34)(35,47)(37,46)(39,41)(43,45);(16,19,22,35)(17,24,28,41)(18,30,33,47)(20,34,21,37)(23,38,40,39)(25,27,43,26)(29,45,44,42)(31,32,46,36);(16,19)(17,25)(18,31)(20,37)(21,34)(22,35)(23,39)(24,26)(27,41)(28,43)(29,45)(30,36)(32,47)(33,46)(38,40)(42,44)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15884);