Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24987 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#24987 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2420 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
638 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,24)(20,28)(21,32)(22,34)(26,41)(27,37)(30,31)(33,45)(35,39)(38,46)(42,43)(48,49);(18,19,22,24,23,27,34,37)(20,25,28,39,31,40,30,35)(21,26,32,36,33,41,45,47)(29,38,42,48,44,49,43,46);(18,20)(19,25)(21,29)(22,30)(23,31)(24,35)(26,38)(27,40)(28,34)(32,43)(33,44)(36,46)(37,39)(41,49)(42,45)(47,48);(18,21,22,32,23,33,34,45)(19,26,24,36,27,41,37,47)(20,29,30,43,31,44,28,42)(25,38,35,46,40,49,39,48)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17975);