Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#1839 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C23 |
| commutator | C22 | C22×C8×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| socle, prime radical | C23×C17 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
240 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,25)(21,23)(22,24)(26,27)(28,30)(29,31)(32,33)(34,35,36,38,37,39,40,41);(18,20,22,21)(19,23,24,25)(26,28,29,32)(27,30,31,33);(18,21,22,20)(19,23,24,25)(27,31)(30,33)952 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 571);