Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#3509 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| prime radical | C2×#41×C17 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
992 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(20,24)(22,25)(26,27,30,33)(28,31,36,34)(29,37,38,32)(35,40,41,39);(18,19,21,23)(20,22,24,25)(26,27)(28,34)(29,32)(30,33)(31,36)(35,40)(37,38)(39,41);(18,20,21,24)(19,22,23,25);(26,28)(27,31)(29,35)(30,36)(32,39)(33,34)(37,40)(38,41);(26,29,30,38)(27,32,33,37)(28,35,36,41)(31,39,34,40)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2241);