Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#2916 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C22×D4 |
| commutator | C4 | C23×C4×C17 |
| Frattini, cosocle | C2×C4 | C24×C17 |
| socle | C2×C17 | C22×C4⋊C4 |
| prime radical | C2×#41×C17 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C2×#41×C17 ◁ G | |
440 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,27,24,28,22,37)(20,29,32,39,33,43,31,25)(21,26,36,41,34,40,35,47)(30,42,46,48,44,49,45,38);(18,20,22,31,24,33,23,32)(19,25,27,29,28,39,37,43)(21,30,35,45,34,44,36,46)(26,38,41,42,40,48,47,49);(18,21)(19,26)(20,30)(22,35)(23,36)(24,34)(25,38)(27,41)(28,40)(29,42)(31,45)(32,46)(33,44)(37,47)(39,48)(43,49);(21,34)(26,40)(30,44)(35,36)(38,48)(41,47)(42,49)(45,46)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1648);