Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3008 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#3011 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C17 |
| prime radical | C2×C17×2−1+4 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×#41×C17 ◁ G | |
700 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,27,31)(24,32,35,45)(25,29,36,43)(26,38,40,30)(28,39,42,34)(33,46,47,53)(37,50,49,44)(41,51,52,48);(22,24,27,35)(23,28,31,42)(25,33,36,47)(26,39,40,34)(29,41,43,52)(30,45,38,32)(37,51,49,48)(44,53,50,46);(19,21)(22,25)(23,29)(24,33)(26,37)(27,36)(28,41)(30,44)(31,43)(32,46)(34,48)(35,47)(38,50)(39,51)(40,49)(42,52)(45,53);(25,36)(29,43)(33,47)(37,49)(41,52)(44,50)(46,53)(48,51)544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1743);