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×#2245 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C17 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C17 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ C4×C8×C17 ◁ G | |
132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 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)(26,27,33,39)(28,35,43,54)(29,34,45,52)(30,37,47,49)(31,36,40,55)(32,48,46,38)(41,53,56,51)(42,57,44,50);(19,22)(23,25)(26,28,40,56,32,42,30,29,33,43,31,41,46,44,47,45)(27,34,49,57,38,51,36,35,39,52,37,50,48,53,55,54);(18,20,21,24)(19,23,22,25)(26,29,30,44,46,56,40,43,33,45,47,42,32,41,31,28)(27,35,36,53,48,57,49,52,39,54,55,51,38,50,37,34)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 977);