Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60252 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C22×C17 | C24×C4 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ 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)(34,35,38,42,39,43,49,55)(36,40,46,52,45,51,58,62)(37,41,48,54,47,53,59,63)(44,50,57,61,56,60,64,65);(18,20,22,28)(19,23,25,26)(21,29,30,27)(24,32,33,31)(34,36)(35,40)(37,44)(38,46)(39,45)(41,50)(42,52)(43,51)(47,56)(48,57)(49,58)(53,60)(54,61)(55,62)(59,64)(63,65);(18,21,22,30)(19,24,25,33)(20,27,28,29)(23,31,26,32)(34,37)(35,41)(36,44)(38,48)(39,47)(40,50)(42,54)(43,53)(45,56)(46,57)(49,59)(51,60)(52,61)(55,63)(58,64)(62,65);(19,25)(23,26)(24,33)(31,32)(37,47)(41,53)(44,56)(48,59)(50,60)(54,63)(57,64)(61,65);(36,45)(40,51)(44,56)(46,58)(50,60)(52,62)(57,64)(61,65)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53240);