Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9303 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9304 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C23×C17 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
436 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
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)(19,23)(20,21)(24,25)(26,27)(28,32,37,47)(29,39)(30,42)(31,34)(33,40)(35,44)(36,50,51,57)(38,54,53,46)(41,49)(43,48)(45,55,56,52);(18,19,21,23,22,25,20,24)(26,28)(27,32,34,47)(29,36)(30,38)(31,37)(33,45,48,56)(35,46,42,54)(39,50,49,57)(40,52)(41,51)(43,55)(44,53);(18,20,22,21)(19,24,25,23)(26,29,31,41)(27,33,34,48)(28,36,37,51)(30,43,44,40)(32,45,47,56)(35,49,42,39)(38,55,53,52)(46,57,54,50)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2292);