Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13024 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #447 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1879 |
| prime radical | C17×#3414 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C2×C17×#97 ◁ G | |
466 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,24,30,25,31,23,42,26,32,43,49,41,48,22,29)(20,33,34,46,35,47,21,37,36,28,39,27,38,44,40,45);(18,20,25,38,26,36,41,35)(19,27,31,37,32,46,48,45)(21,23,34,43,40,22,39,24)(28,29,47,30,33,42,44,49);(18,21)(19,28)(20,23)(22,36)(24,35)(25,34)(26,40)(27,29)(30,37)(31,47)(32,33)(38,43)(39,41)(42,46)(44,48)(45,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6012);