Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#2769 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C17 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
344 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
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)(18,19,22,20)(21,24,25,23)(26,27)(28,31)(29,30)(32,33)(36,39)(37,41);(19,20)(21,25)(27,29)(31,32)(34,35,38,40)(36,37,39,41);(18,20,22,19)(21,24,25,23)(26,28,30,33)(27,31,29,32)(34,36,38,39)(35,37,40,41);(18,21,22,25)(19,23,20,24)(26,29,30,27)(28,32,33,31)(34,37)(35,39)(36,40)(38,41)544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1501);