Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#60108 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C4 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C22×C17 | C23×D4 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×#41×C17 ◁ G | |
2666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 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)(24,33)(25,30)(26,31)(27,41)(28,32)(29,36)(34,46)(35,43)(37,47)(38,44)(39,45)(40,51)(42,50)(48,53)(49,52);(22,24,27,36,28,37,26,35)(23,29,31,33,32,43,41,47)(25,34,40,50,38,48,39,49)(30,42,45,46,44,52,51,53);(22,25)(23,30)(24,34)(26,39)(27,40)(28,38)(29,42)(31,45)(32,44)(33,46)(35,49)(36,50)(37,48)(41,51)(43,52)(47,53);(25,38)(30,44)(34,48)(39,40)(42,52)(45,51)(46,53)(49,50);(22,26,28,27)(23,31,32,41)(24,35,37,36)(25,39,38,40)(29,33,43,47)(30,45,44,51)(34,49,48,50)(42,46,52,53)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53096);