Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61862 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#449 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#533 ◁ G | |
1614 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 65 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26)(21,24)(22,25)(23,28)(27,32)(29,31)(30,33)(34,35,39,44)(36,46,48,41)(37,50,52,59)(38,45,40,43)(42,54,57,51)(47,61,62,65)(49,56,53,58)(55,64,60,63);(18,20,22,28)(19,23,25,26)(21,29,30,27)(24,32,33,31)(34,36,39,48)(35,41,44,46)(37,47,52,62)(38,53,40,49)(42,55,57,60)(43,58,45,56)(50,65,59,61)(51,64,54,63);(34,37)(35,42)(36,47)(38,51)(39,52)(40,54)(41,55)(43,50)(44,57)(45,59)(46,60)(48,62)(49,63)(53,64)(56,61)(58,65);(18,21,22,30)(19,24,25,33)(20,27,28,29)(23,31,26,32)(36,48)(41,46)(47,62)(49,53)(55,60)(56,58)(61,65)(63,64);(19,25)(23,26)(24,33)(31,32)(34,38,39,40)(35,43,44,45)(36,49,48,53)(37,51,52,54)(41,56,46,58)(42,50,57,59)(47,63,62,64)(55,61,60,65)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54850);