Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#1422 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C17 | D4 |
| commutator | C4 | C2×C16×C17 |
| Frattini, cosocle | C2×C16 | C22×C17 |
| socle | C2×C17 | C4⋊C16 |
| prime radical | C22×C17 | M32 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C17 ◁ C2×C16×C17 ◁ G | |
58 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)(18,19,22,28,23,29,37,44,24,27,38,42,34,43,47,49,25,30,39,45,32,26,40,41,21,35,36,48,20,31,33,46);(18,20,21,32,25,34,24,23)(19,26,27,31,30,29,35,43)(22,33,36,40,39,47,38,37)(28,41,42,46,45,44,48,49)952 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 154);