Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C8 |
| direct product | C17×#1455 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C17 | C23 |
| commutator | C22 | C2×C42×C17 |
| Frattini, cosocle | C42 | C23×C17 |
| socle | C22×C17 | C2×C42 |
| prime radical | C23×C17 | C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C17 ◁ G | |
214 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,23,21,22,24,25);(26,27,28,31,29,30,32,33);(19,22)(23,25)(27,30)(31,33)952 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 187);