Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#2527 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C17 |
| prime radical | C24×C17 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
420 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 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)(20,22,24,25)(26,27)(28,32)(29,31)(30,33)(36,40)(39,41);(18,19,21,23)(20,22,24,25)(26,27,29,31)(28,30,33,32)(34,35,38,37)(36,39,40,41);(18,19)(20,22)(21,23)(24,25)(26,27)(28,30)(29,31)(32,33)(34,36)(35,39)(37,41)(38,40);(18,20,21,24)(19,22,23,25)(26,28)(27,30)(29,33)(31,32)(34,37,38,35)(36,41,40,39)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1259);