Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#2253 |
| 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 | |
116 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)(18,19,21,23)(20,24,25,22)(26,27,29,32)(28,36,38,50)(30,43,41,56)(31,44,42,35)(33,47,45,39)(34,49,46,37)(40,55,54,52)(48,53,51,57);(18,20,21,25)(19,22,23,24)(27,32)(33,45)(34,46)(35,44)(36,50)(43,56)(48,51)(52,55);(26,28,37,53,31,40,41,47,29,38,49,57,42,54,30,39)(27,33,43,52,35,48,46,50,32,45,56,55,44,51,34,36)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 985);