Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#1369 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #106 |
| commutator | C8 | C2×C8×C17 |
| Frattini, cosocle | C4×C8 | C22×C17 |
| socle | C2×C17 | #334 |
| prime radical | C22×C17 | #108 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C2×C8×C17 ◁ C4×C8×C17 ◁ G | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 2 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,28,24,29,39,45,25,30,38,27,23,41,21,37)(20,31,33,42,35,46,32,43,36,44,40,49,34,48,47,26);(18,20,21,32,23,34,38,33,25,36,39,47,24,35,22,40)(19,26,27,31,29,42,37,46,30,43,28,44,41,49,45,48)544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 101);