Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#21006 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 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)(22,23,27,33,28,32,26,31)(24,29,37,44,36,45,35,43)(25,38,39,30,40,46,41,47)(34,48,49,42,51,52,50,53);(22,24,26,37,28,36,27,35)(23,29,33,43,32,45,31,44)(25,34,39,50,40,51,41,49)(30,42,38,52,47,53,46,48);(19,21)(22,25)(23,30)(24,34)(26,39)(27,41)(28,40)(29,42)(31,46)(32,47)(33,38)(35,49)(36,51)(37,50)(43,52)(44,48)(45,53);(22,26,28,27)(23,31,32,33)(24,35,36,37)(25,39,40,41)(29,43,45,44)(30,46,47,38)(34,49,51,50)(42,52,53,48)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13994);