Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13009 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #481 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C24×C17 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C22×M16×C17 ◁ G | |
496 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)(22,23,26,32,43,45,40,31,28,30,41,49,27,33,25,39)(24,34,37,29,44,47,35,51,36,52,53,46,38,50,42,48);(18,19,20,21)(22,24,27,44,28,36,43,38)(23,29,45,48,30,46,33,51)(25,37,41,35,40,53,26,42)(31,50,49,52,39,47,32,34);(23,30)(25,40)(26,41)(29,46)(33,45)(35,42)(37,53)(48,51)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5997);