Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#19013 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#3531 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 2176 |
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)(22,30)(23,26)(24,28)(29,32)(31,33)(34,35,40,43)(36,46,49,58)(37,50,52,59)(38,45,39,44)(41,53,56,48)(42,54,57,51)(47,55,63,65)(60,61,64,62);(18,19)(20,24)(21,25)(22,30)(23,26)(27,31)(28,32)(29,33)(34,36,40,49)(35,41,43,56)(37,47,52,63)(38,53,39,48)(42,55,57,65)(44,58,45,46)(50,64,59,60)(51,62,54,61);(18,20)(19,24)(21,28)(22,31)(23,29)(25,32)(26,33)(27,30)(34,37)(35,42)(36,47)(38,51)(39,54)(40,52)(41,55)(43,57)(44,50)(45,59)(46,60)(48,61)(49,63)(53,62)(56,65)(58,64);(18,21,23,22)(19,25,26,30)(20,28,29,31)(24,32,33,27)(35,43)(41,56)(42,57)(44,45)(46,58)(50,59)(55,65)(60,64)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12001);