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×#3538 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| prime radical | C17×#525 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
1014 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)(19,22)(20,24)(26,27,31,33)(28,34,36,29)(30,38,39,32)(35,37,41,40);(19,22)(23,25)(26,28,31,36)(27,29,33,34)(30,35,39,41)(32,37,38,40);(18,19)(20,23)(21,22)(24,25);(18,20)(19,23)(21,24)(22,25)(26,29)(27,28)(30,37)(31,34)(32,35)(33,36)(38,41)(39,40);(26,30,31,39)(27,32,33,38)(28,35,36,41)(29,37,34,40)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2270);