Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#19060 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#3553 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
822 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)(20,26)(21,28)(23,31)(24,29)(27,30)(32,33)(34,35,40,45)(36,46,49,58)(37,50,51,59)(38,44,39,43)(41,53,56,48)(42,54,57,52)(47,55,61,65)(60,62,64,63);(18,19,22,25)(20,23,27,32)(21,29,28,24)(26,33,30,31)(34,36)(35,41)(37,47)(38,53)(39,48)(40,49)(42,55)(43,58)(44,46)(45,56)(50,64)(51,61)(52,63)(54,62)(57,65)(59,60);(18,20)(19,23)(21,30)(22,27)(24,33)(25,32)(26,28)(29,31)(34,37)(35,42)(36,47)(38,52)(39,54)(40,51)(41,55)(43,50)(44,59)(45,57)(46,60)(48,62)(49,61)(53,63)(56,65)(58,64);(37,51)(42,57)(47,61)(50,59)(52,54)(55,65)(60,64)(62,63)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12048);