Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13033 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13036 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1879 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
476 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)(18,19,24,29,31,34,23,28,26,30,42,43,25,20,22,33)(21,35,38,27,44,45,36,32,40,48,41,47,39,49,37,46);(18,20,31,30,26,34,25,19)(21,32,39,47,40,46,44,27)(22,33,24,43,23,28,42,29)(35,38,45,37,48,41,49,36);(18,21)(19,27)(20,32)(22,41)(23,38)(24,36)(25,44)(26,40)(28,45)(29,48)(30,47)(31,39)(33,49)(34,46)(35,43)(37,42)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6024);