Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13022 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
494 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)(19,21)(22,23,25,31,42,46,26,32,28,34,43,47,27,33,40,29)(24,35,36,30,44,48,41,52,39,51,53,50,38,45,37,49);(18,19,20,21)(23,29)(25,40)(26,43)(27,42)(30,45)(31,33)(32,34)(35,49)(36,37)(38,44)(41,53)(46,47)(48,50)(51,52);(22,24)(23,30)(25,41)(26,36)(27,44)(28,39)(29,45)(31,51)(32,48)(33,52)(34,50)(35,47)(37,43)(38,42)(40,53)(46,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6010);