Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of AΣL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1328 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #99 |
| commutator | C23 | C2×C8×C17 |
| Frattini, cosocle | C2×M16 | C22×C17 |
| socle | C2×C17 | #324 |
| prime radical | C23×C17 | C2×C8 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C2×C4×C17 ◁ C2×M16×C17 ◁ G | |
90 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)(18,19,21,26,22,27,32,40,23,25,31,37,33,38,44,47)(20,24,29,34,30,36,43,45,28,35,41,39,42,46,49,48);(18,20)(19,24,25,35)(21,29)(22,30)(23,28)(26,39,37,34)(27,36,38,46)(31,41)(32,43)(33,42)(40,48,47,45)(44,49)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 60);