Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18374 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C23×C17 | C22×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
838 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)(18,19)(20,27)(21,25)(22,31)(23,26)(24,29)(28,32)(30,33)(34,35,39,43)(36,40,46,53)(37,41,48,55)(38,49,50,42)(44,56,58,51)(45,59,60,52)(47,61,62,54)(57,63,65,64);(18,20,23,30)(19,24,26,32)(21,29,22,28)(25,33,31,27)(34,36)(35,40)(37,44)(38,45)(39,46)(41,51)(42,52)(43,53)(47,57)(48,58)(49,59)(50,60)(54,63)(55,56)(61,64)(62,65);(34,37,39,48)(35,41,43,55)(36,44,46,58)(38,47,50,62)(40,51,53,56)(42,54,49,61)(45,57,60,65)(52,63,59,64);(18,21,23,22)(19,25,26,31)(20,28,30,29)(24,27,32,33)(34,38,39,50)(35,42,43,49)(36,45,46,60)(37,47,48,62)(40,52,53,59)(41,54,55,61)(44,57,58,65)(51,63,56,64)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11362);