Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#13412 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
430 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)(13,14)(16,17)(18,23)(19,24)(20,37)(21,38)(22,27)(25,34)(26,35)(28,46)(29,42)(30,47)(31,40)(32,44)(33,41)(36,45)(39,43);(12,13)(14,15)(16,18,22,32)(17,23,27,44)(19,33,36,30)(20,28,34,29)(21,39,35,31)(24,41,45,47)(25,42,37,46)(26,40,38,43);(12,14,15,13)(17,24)(18,28)(19,34)(20,36)(21,35)(23,40)(25,26)(27,45)(29,32)(30,39)(31,33)(37,38)(42,46)(43,44)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6400);