Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1412 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1413 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #354 |
| commutator | C42 | C2×C4×C17 |
| Frattini, cosocle | C4⋊Q8 | C22×C17 |
| prime radical | C22×C17 | #99 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C17 ◁ C2×C4×C17 ◁ C17×C4⋊Q8 ◁ G | |
78 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)(18,19,21,26,23,28,35,45)(20,29,31,47,30,46,48,43)(22,27,37,44,38,25,34,42)(24,39,40,32,41,33,49,36);(18,20,23,30)(19,24)(21,33,35,39)(22,36,38,32)(25,29)(26,43)(27,46)(28,41)(31,34,48,37)(40,42)(44,49)(45,47)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 145);