Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60753 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60869 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C17×#117 ◁ G | |
1626 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 1088 |
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)(34,35,40,45)(36,41,47,55)(37,50,52,59)(38,44,39,43)(42,53,58,51)(46,60,61,65)(48,57,49,56)(54,63,64,62);(18,20,22,28)(19,23,25,26)(21,29,30,27)(24,32,33,31)(34,36)(35,41)(37,46)(38,48)(39,49)(40,47)(42,54)(43,56)(44,57)(45,55)(50,60)(51,62)(52,61)(53,63)(58,64)(59,65);(18,21,22,30)(19,24,25,33)(20,27,28,29)(23,31,26,32)(34,37)(35,42)(36,46)(38,51)(39,53)(40,52)(41,54)(43,50)(44,59)(45,58)(47,61)(48,62)(49,63)(55,64)(56,60)(57,65);(19,25)(23,26)(24,33)(31,32)(36,47)(41,55)(46,61)(48,49)(54,64)(56,57)(60,65)(62,63);(34,38,40,39)(35,43,45,44)(36,48,47,49)(37,51,52,53)(41,56,55,57)(42,50,58,59)(46,62,61,63)(54,60,64,65)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53857);