Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2218 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C4 |
| direct product | C17×#2244 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C17 |
| prime radical | C17×#493 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ C4×C8×C17 ◁ G | |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(27,33)(28,39)(29,34)(30,41)(31,35)(36,37)(38,40);(19,22)(23,25)(26,27,34,28,31,37,41,40,32,38,30,36,35,39,29,33);(18,20,21,24)(19,23,22,25)(26,28,29,27,35,33,30,39,32,36,41,38,31,40,34,37)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 976);