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×#3502 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| prime radical | C23×C17 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
964 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)(18,19,21,23)(20,24,25,22)(26,27,31,35)(28,33,29,32)(30,34,38,41)(36,40,37,39);(26,28,31,29)(27,32,35,33)(30,37,38,36)(34,40,41,39);(18,20,21,25)(19,22,23,24)(26,29,31,28)(27,33,35,32)(30,37,38,36)(34,40,41,39);(26,30,31,38)(27,34,35,41)(28,36,29,37)(32,39,33,40);(26,27)(28,32)(29,33)(30,34)(31,35)(36,39)(37,40)(38,41)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2234);