Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#3177 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C17 |
| prime radical | C23×C17 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#117 ◁ G | |
338 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 57 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)(26,27,31,35)(28,32,37,45)(29,39,42,54)(30,43,40,34)(33,47,48,41)(36,49,51,57)(38,53,50,46)(44,55,56,52);(19,22)(23,25)(26,28,31,37)(27,32,35,45)(29,36,42,51)(30,38,40,50)(33,44,48,56)(34,46,43,53)(39,49,54,57)(41,52,47,55);(26,29,40,47,31,42,30,41)(27,33,43,54,35,48,34,39)(28,36,50,55,37,51,38,52)(32,44,53,57,45,56,46,49);(18,20,21,24)(19,23,22,25)(28,37)(32,45)(36,51)(38,50)(44,56)(46,53)(49,57)(52,55)544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1909);