Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9671 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #121 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | #390 |
| prime radical | C23×C17 | C4×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
434 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,24,22,20,21,25)(26,27)(28,32,37,46)(29,39)(30,42)(31,34)(33,40)(35,43)(36,48,49,57)(38,52,51,45)(41,53)(44,55,56,50)(47,54);(18,20,23,25,22,19,21,24)(26,28,31,37)(27,32)(29,36,41,49)(30,38,43,51)(33,44)(34,46)(35,45)(39,48)(40,50,54,55)(42,52)(47,56)(53,57);(18,21,22,23)(19,24,20,25)(26,29,30,40,31,41,43,54)(27,33,35,39,34,47,42,53)(28,36,38,50,37,49,51,55)(32,44,45,48,46,56,52,57)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2659);