Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#3564 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| prime radical | C17×#538 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
936 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,27)(20,28,29,25)(21,32,35,26)(22,24,34,38)(30,40,42,41)(31,39,43,36)(33,46,47,37)(44,49,45,48);(19,24)(20,29)(21,33)(25,39)(27,38)(28,36)(30,44)(31,43)(35,47)(40,41)(42,45)(48,49);(18,20,22,31)(19,25,24,36)(21,30,33,45)(23,29,34,43)(26,40,37,48)(27,28,38,39)(32,41,46,49)(35,42,47,44);(18,21,34,47)(19,26,38,46)(20,30,43,44)(22,33,23,35)(24,37,27,32)(25,40,39,49)(28,41,36,48)(29,42,31,45);(19,24)(25,36)(26,37)(27,38)(28,39)(32,46)(40,48)(41,49)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2296);