Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#21077 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(22,23)(24,33)(25,37)(26,31)(27,42)(28,32)(29,35)(30,40)(34,48)(36,44)(38,52)(39,46)(41,45)(43,53)(47,50)(49,51);(18,20,21,19)(22,24,27,35,28,36,26,41)(23,29,31,33,32,45,42,44)(25,34,39,49,40,50,38,53)(30,43,46,47,37,51,52,48);(22,25,27,39,28,40,26,38)(23,30,31,46,32,37,42,52)(24,34,35,49,36,50,41,53)(29,43,33,47,45,51,44,48);(22,26,28,27)(23,31,32,42)(24,35,36,41)(25,38,40,39)(29,44,45,33)(30,46,37,52)(34,49,50,53)(43,48,51,47)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14065);