Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#1380 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | D8 |
| commutator | C8 | C42×C17 |
| Frattini, cosocle | C22×C8 | C22×C17 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C22×C4×C17 ◁ C22×C8×C17 ◁ G | |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 2 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,24,25)(27,32)(28,36)(29,38)(30,37)(33,34)(35,41)(39,40);(19,21)(26,27,29,33,30,34,28,32,31,35,36,40,37,39,38,41)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 112);