Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#2324 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C24 |
| commutator | C22 | C23×C4×C17 |
| Frattini, cosocle | C23 | C24×C17 |
| prime radical | C2×C17×#121 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
668 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23,25,24)(26,27,29,30)(28,32,33,31);(22,24,25,23)(27,30)(31,32);(18,19)(20,21)(26,27)(28,31)(29,30)(32,33);(26,28,29,33)(27,31,30,32)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1056);