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×#24988 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2420 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#472 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
656 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)(21,33)(22,34)(26,41)(27,38)(31,32)(35,46)(36,40)(39,47)(42,44)(43,49);(18,19,22,24,23,27,34,38)(20,29,28,36,32,25,31,40)(21,26,33,37,35,41,46,48)(30,43,42,47,45,39,44,49);(18,20)(19,25)(21,30)(22,31)(23,32)(24,36)(26,39)(27,29)(28,34)(33,44)(35,45)(37,47)(38,40)(41,43)(42,46)(48,49);(18,21,34,46,23,35,22,33)(19,26,38,48,27,41,24,37)(20,30,28,42,32,45,31,44)(25,39,40,49,29,43,36,47)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17976);