Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#21547 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C17×#3050 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×M16×C17 ◁ G | |
906 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)(20,21)(22,23,27,31,28,32,26,42)(24,33,36,44,37,49,35,29)(25,30,41,47,39,46,40,53)(34,48,51,45,38,52,50,43);(22,24,26,35,28,37,27,36)(23,29,31,33,32,44,42,49)(25,38,40,51,39,34,41,50)(30,45,47,52,46,43,53,48);(19,21)(25,39)(30,46)(34,38)(40,41)(43,45)(47,53)(48,52)(50,51);(22,25,27,41,28,39,26,40)(23,30,31,47,32,46,42,53)(24,34,36,51,37,38,35,50)(29,43,33,48,44,45,49,52)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14535);