Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61877 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C2×#41×C17 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#533 ◁ G | |
1600 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)(34,35,40,43)(36,41,46,57)(37,48,50,59)(38,44,39,52)(42,53,58,49)(45,60,61,65)(47,55,51,56)(54,62,64,63);(18,20,22,28)(19,23,25,26)(21,29,30,27)(24,32,33,31)(34,36)(35,41)(37,45)(38,51)(39,47)(40,46)(42,54)(43,57)(44,56)(48,60)(49,63)(50,61)(52,55)(53,62)(58,64)(59,65);(34,37)(35,42)(36,45)(38,49)(39,53)(40,50)(41,54)(43,58)(44,59)(46,61)(47,62)(48,52)(51,63)(55,60)(56,65)(57,64);(18,21,22,30)(19,24,25,33)(20,27,28,29)(23,31,26,32)(35,43)(36,46)(42,58)(44,52)(45,61)(47,51)(48,59)(62,63);(19,25)(23,26)(24,33)(31,32)(34,38,40,39)(35,44,43,52)(36,47,46,51)(37,49,50,53)(41,55,57,56)(42,59,58,48)(45,62,61,63)(54,60,64,65)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54865);