Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18443 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#121 | C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
832 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 65 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,24)(21,22)(25,32)(26,30)(27,28)(31,33)(34,35,39,43)(36,44,47,57)(37,41,48,55)(38,50,52,42)(40,51,54,46)(45,58,59,65)(49,62,61,56)(53,63,64,60);(18,19,23,26)(20,25,29,33)(21,24,22,30)(27,32,28,31)(34,36,39,47)(35,40,43,54)(37,45,48,59)(38,51,52,46)(41,53,55,64)(42,57,50,44)(49,63,61,60)(56,65,62,58);(18,20,23,29)(19,25,26,33)(21,28,22,27)(24,31,30,32)(34,37,39,48)(35,41,43,55)(36,45,47,59)(38,49,52,61)(40,53,54,64)(42,56,50,62)(44,58,57,65)(46,60,51,63);(18,21,23,22)(19,24,26,30)(20,27,29,28)(25,32,33,31)(37,48)(41,55)(45,59)(49,61)(53,64)(56,62)(58,65)(60,63)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11431);