Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#21476 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×2−1+4 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
1322 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)(18,19,21,20)(22,23,27,31)(24,32,35,46)(25,29,36,44)(26,38,41,30)(28,39,43,34)(33,49,50,48)(37,47,40,45)(42,52,53,51);(22,24)(23,28)(25,33)(26,39)(27,35)(29,42)(30,46)(31,43)(32,38)(34,41)(36,50)(37,52)(40,51)(44,53)(45,48)(47,49);(22,25,27,36)(23,29,31,44)(24,33,35,50)(26,40,41,37)(28,42,43,53)(30,47,38,45)(32,48,46,49)(34,52,39,51);(18,20,21,19)(25,36)(29,44)(33,50)(37,40)(42,53)(45,47)(48,49)(51,52)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14464);