Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25×C4 |
| direct product | C17×#21248 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #121 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C2×#121 |
| prime radical | C22×C17×#135 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
1458 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)(19,21)(22,23,27,33,28,32,26,31)(24,29,35,43,36,45,41,44)(25,37,39,47,40,46,38,30)(34,48,49,42,50,52,51,53);(18,19,20,21)(22,24,27,41,28,36,26,35)(23,29,31,43,32,45,33,44)(25,34,39,51,40,50,38,49)(30,42,46,52,47,53,37,48);(22,25,26,38,28,40,27,39)(23,30,33,37,32,47,31,46)(24,34,35,49,36,50,41,51)(29,42,44,48,45,53,43,52);(22,26,28,27)(23,31,32,33)(24,35,36,41)(25,38,40,39)(29,43,45,44)(30,46,47,37)(34,49,50,51)(42,52,53,48)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14236);