Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13023 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
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)(22,23,27,33,42,51,26,30,29,35,25,32,28,34,43,47)(24,36,39,31,45,46,44,53,41,52,37,50,40,48,38,49);(18,19,20,21)(23,30)(25,26)(27,43)(28,42)(31,46)(32,34)(33,51)(35,47)(36,53)(37,44)(38,39)(40,45)(48,50)(49,52);(22,24)(23,31)(25,38)(26,39)(27,44)(28,45)(29,41)(30,46)(32,36)(33,52)(34,53)(35,50)(37,43)(40,42)(47,48)(49,51)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6011);