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×C4 |
| direct product | C17×#2247 |
| 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 | |
176 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23,27,31)(24,32,36,48)(25,37,39,52)(26,40,38,30)(28,41,43,34)(29,44,45,33)(35,51,50,47)(42,49,46,53);(22,24,33,49,26,35,39,41,27,36,44,53,38,50,25,34)(23,28,37,47,30,42,45,48,31,43,52,51,40,46,29,32);(18,19,20,21)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 979);