Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13026 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C17×#97 ◁ G | |
486 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)(22,23,26,31,41,50,42,51,28,33,25,30,27,32,43,52)(24,34,36,46,44,49,39,29,38,45,35,53,37,48,40,47);(18,19,20,21)(22,24)(23,29)(25,39)(26,40)(27,44)(28,38)(30,48)(31,49)(32,53)(33,47)(34,51)(35,42)(36,43)(37,41)(45,52)(46,50);(22,24)(23,29)(25,40)(26,39)(27,44)(28,38)(30,49)(31,48)(32,53)(33,47)(34,52)(35,43)(36,42)(37,41)(45,51)(46,50)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6014);