Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of #7529 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#7530 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1408 |
| commutator | C4×C8 | C2×C4×C17 |
| Frattini, cosocle | #493 | C22×C17 |
| prime radical | C17×#493 | C22 |
| LCS | G ▷ C4×C8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C17 ◁ C2×C4×C17 ◁ C42×C17 ◁ C17×#493 ◁ G | |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 2 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28,30,45)(21,32,35,42)(22,27)(23,26,34,44)(24,29,38,48)(25,36,41,47)(31,46,37,40)(33,43)(39,49);(18,20,22,31)(19,24,27,38)(21,33,36,49)(23,37,34,30)(25,40,42,45)(26,43,44,39)(28,32,46,41)(29,47,48,35)425 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 518);