Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C2×C17×#383 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C17 | C23 |
| commutator | C22 | C23×C4×C17 |
| Frattini, cosocle | C23 | C24×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
624 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(3,4,5,6)(9,13)(11,14)(16,19)(17,21);(7,8,10,12)(9,11,13,14)(15,16)(17,20)(18,19)(21,22);(7,9)(8,11)(10,13)(12,14)(15,17,18,21)(16,20,19,22)952 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1014);