Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13018 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C22×D8×C17 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
480 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)(22,23,28,35,31,40,27,39,30,36,26,33,29,24,37,34)(25,41,44,32,48,50,43,38,46,53,42,52,45,49,47,51);(18,19,20,21)(22,24,30,40)(23,31,36,29)(25,38,46,51)(26,35,28,33)(27,39,37,34)(32,45,52,48)(41,47,53,43)(42,49,44,50);(22,25,30,46)(23,32,36,52)(24,38,40,51)(26,43,28,47)(27,42,37,44)(29,48,31,45)(33,53,35,41)(34,50,39,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6006);