Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C25×C4 |
| direct product | C17×#10759 |
| 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 | C22×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×M16×C17 ◁ G | |
1202 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)(18,19)(20,21)(22,23)(24,34)(25,39,41,30)(26,33)(27,31)(28,32)(29,36)(35,49,51,48)(37,44)(38,45)(40,46,42,47)(43,50,53,52);(19,21)(22,24,27,37,28,38,26,36)(23,29,33,45,32,44,31,34)(25,35,42,52,41,51,40,50)(30,43,47,49,39,53,46,48);(22,25)(23,30)(24,35)(26,40)(27,42)(28,41)(29,43)(31,46)(32,39)(33,47)(34,48)(36,50)(37,52)(38,51)(44,53)(45,49)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3747);