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×#3510 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| prime radical | C17×#535 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
1040 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
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)(28,32)(29,36)(30,31)(33,37)(34,40)(35,38)(39,41);(18,19,21,23)(20,22,24,25)(27,31)(32,38)(33,36)(39,40);(18,20,21,24)(19,22,23,25)(26,28,30,35)(27,32,31,38)(29,34,37,41)(33,39,36,40);(26,27)(28,32)(29,33)(30,31)(34,39)(35,38)(36,37)(40,41);(26,29,30,37)(27,33,31,36)(28,34,35,41)(32,39,38,40)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2242);