Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#10952 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
890 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
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)(24,29,35,44)(25,37)(26,33)(27,32)(28,31)(30,39)(34,48,50,51)(36,47,41,43)(38,45)(40,46)(42,52,53,49);(22,24,27,36,28,35,26,41)(23,29,33,43,31,44,32,47)(25,34,40,49,38,50,39,52)(30,42,45,48,46,53,37,51);(18,19,20,21)(22,25,26,39,28,38,27,40)(23,30,32,37,31,46,33,45)(24,34,41,52,35,50,36,49)(29,42,47,51,44,53,43,48)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3940);