Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#10940 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
898 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 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)(24,28,33,40)(25,29)(26,37)(27,30)(31,38)(32,44,45,39)(34,48,47,41)(35,43)(36,50)(42,49)(46,51,53,52);(22,24,26,34,27,33,38,47)(23,28,31,41,30,40,37,48)(25,32,36,46,35,45,49,53)(29,39,42,51,43,44,50,52);(18,19,20,21)(22,25,27,35)(23,29,30,43)(24,32,33,45)(26,36,38,49)(28,39,40,44)(31,42,37,50)(34,46,47,53)(41,51,48,52)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3928);