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×#10920 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #385 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
698 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)(22,23,26,30,27,31,37,43)(24,28,34,40,33,39,47,51)(25,29,36,42,35,41,48,52)(32,44,46,53,45,38,49,50);(18,19,20,21)(22,24)(23,28)(25,32)(26,34)(27,33)(29,38)(30,40)(31,39)(35,45)(36,46)(37,47)(41,44)(42,50)(43,51)(48,49)(52,53);(22,25,26,36,27,35,37,48)(23,29,30,42,31,41,43,52)(24,32,34,46,33,45,47,49)(28,38,40,50,39,44,51,53)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3908);