Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13005 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13007 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1874 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
492 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)(18,19,24,30,23,29,40,28,26,31,39,42,25,20,22,33)(21,32,36,47,41,27,38,45,37,48,43,44,35,46,34,49);(18,20,23,31,26,29,25,19)(21,32,41,46,37,48,35,27)(22,33,24,42,40,28,39,30)(34,47,36,49,38,44,43,45);(18,21)(19,27)(20,32)(22,38)(23,41)(24,43)(25,35)(26,37)(28,47)(29,48)(30,49)(31,46)(33,44)(34,40)(36,39)(42,45)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5995);