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×#3507 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| prime radical | C17×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
1012 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)(20,24)(22,25)(26,27)(28,35)(29,30)(31,32)(33,38)(34,39)(36,41)(37,40);(18,19,21,23)(20,22,24,25)(27,32)(29,34)(33,35)(36,40);(18,20,21,24)(19,22,23,25)(26,28,31,38)(27,33,32,35)(29,36,34,40)(30,37,39,41);(26,29,31,34)(27,30,32,39)(28,36,38,40)(33,37,35,41);(26,30)(27,34)(28,37)(29,32)(31,39)(33,40)(35,36)(38,41)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2239);