Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C4 |
| direct product | C17×#1407 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #353 |
| commutator | C42 | C2×C4×C17 |
| Frattini, cosocle | #124 | C22×C17 |
| prime radical | C2×D4×C17 | D4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C17 ◁ C2×C4×C17 ◁ C17×#124 ◁ G | |
98 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)(20,28,30,43)(21,32,33,48)(22,35,37,26)(23,27)(24,29,38,45)(25,34)(31,41,36,44)(39,46,40,47)(42,49);(18,20,23,31)(19,24,27,40)(21,29,33,47)(22,36,37,30)(25,41,42,28)(26,38,35,39)(32,44,48,43)(34,45,49,46)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 139);