Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#22691 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
846 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)(24,36)(25,40)(26,32)(27,34)(28,33)(29,35)(30,38)(31,37)(39,52)(41,49)(42,50)(43,48)(44,53)(45,47)(46,51);(22,24)(23,30)(25,26)(27,41)(28,38)(29,39)(31,47)(32,50)(33,52)(34,36)(35,49)(37,44)(40,53)(42,46)(43,45)(48,51);(22,25,27,42,29,43,28,37)(23,31,33,48,35,50,34,40)(24,26,41,46,39,45,38,44)(30,47,52,51,49,32,36,53);(22,26)(23,32)(24,37)(25,41)(27,46)(28,44)(29,45)(30,48)(31,36)(33,53)(34,51)(35,47)(38,43)(39,42)(40,49)(50,52)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 15679);