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×#10961 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | C4×C22⋊C4 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C8×C17 ◁ G | |
926 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)(22,23,26,31,27,30,39,43)(24,28,34,41,33,42,37,46)(25,29,36,44,35,45,38,47)(32,48,49,53,50,40,51,52);(19,21)(22,24)(23,28,30,42)(25,32)(26,37)(27,33)(29,40,45,48)(31,46,43,41)(34,39)(35,50)(36,51)(38,49)(44,53,47,52);(22,25,26,38,27,35,39,36)(23,29,43,44,30,45,31,47)(24,32,37,49,33,50,34,51)(28,40,41,53,42,48,46,52)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3949);