Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C22×C17×C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C17 | C23 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| prime radical | C25×C17 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
1840 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33);(3,4);(6,8)(9,10,12,14)(11,15,16,13);(9,11,12,16)(10,13,14,15);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)952 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2165);