Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3288 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#3289 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C24×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ G | |
448 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)(18,19,24,30)(20,31,35,46)(21,27,37,45)(22,29,23,28)(25,38,42,34)(26,39,43,36)(32,40,49,41)(33,47,48,44);(18,20,24,35)(19,25,30,42)(21,32,37,49)(22,38,23,34)(26,40,43,41)(27,44,45,47)(28,46,29,31)(33,39,48,36);(18,21)(19,26)(20,32)(22,36)(23,39)(24,37)(25,40)(27,28)(29,45)(30,43)(31,47)(33,38)(34,48)(35,49)(41,42)(44,46);(18,21)(19,27)(20,33)(22,39)(23,36)(24,37)(25,41)(26,28)(29,43)(30,45)(31,47)(32,38)(34,49)(35,48)(40,42)(44,46)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2021);