Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#10867 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #117 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #380 |
| prime radical | C24×C17 | C2×Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×M16×C17 ◁ G | |
714 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)(22,23,27,32,28,31,26,41)(24,33,35,44,36,29,42,45)(25,37,39,46,40,52,38,30)(34,48,49,47,50,51,53,43);(18,19,20,21)(22,24)(23,29)(25,34)(26,35)(27,42)(28,36)(30,43)(31,33)(32,44)(37,51)(38,49)(39,53)(40,50)(41,45)(46,47)(48,52);(22,25,26,38,28,40,27,39)(23,30,32,37,31,46,41,52)(24,34,35,49,36,50,42,53)(29,43,44,51,33,47,45,48)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3855);