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×#10873 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #121 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #389 |
| prime radical | C24×C17 | C2×Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×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)(18,19,20,21)(22,23,26,32,28,33,27,31)(24,34,37,45,38,44,36,29)(25,39,40,30,42,46,41,47)(35,43,50,48,51,53,49,52);(22,24,27,36,28,38,26,37)(23,29,31,44,33,45,32,34)(25,35,41,49,42,51,40,50)(30,43,39,52,47,53,46,48);(22,25,26,40,28,42,27,41)(23,30,31,39,33,47,32,46)(24,35,37,50,38,51,36,49)(29,43,44,52,45,53,34,48)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3861);