Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1339 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1340 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #327 |
| commutator | C2×C8 | C2×C4×C17 |
| Frattini, cosocle | C2×M16 | C22×C17 |
| prime radical | C23×C17 | D8 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×M16×C17 ◁ G | |
104 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)(20,29,31,46)(21,34,36,45)(22,27)(23,39)(24,28)(25,30)(26,37,43,38)(32,42,33,49)(35,44)(40,47)(41,48);(18,20,24,31)(19,25,28,41)(21,35,36,47)(22,33,23,32)(26,42,43,49)(27,44,39,40)(29,45,46,34)(30,37,48,38)340 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 72);