Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#1338 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22⋊C4 |
| commutator | C2×C4 | C2×C8×C17 |
| Frattini, cosocle | C4×C8 | C22×C17 |
| socle, prime radical | C22×C17 | C22⋊C8 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C4×C8×C17 ◁ G | |
86 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)(19,22)(20,24)(23,25)(26,27,29,34,31,32,37,39,30,33,38,40,28,35,36,41);(18,19,21,23)(20,25,24,22)(26,28,30,31)(27,32,33,35)(29,37,38,36)(34,41,40,39)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 70);