Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17856 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C4 | C23×C8×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C23×C17 | C4×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C17×#431 ◁ G | |
678 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,24,22,20,23,25)(26,27)(28,36)(29,33)(30,42)(31,34)(32,38)(35,44)(37,50)(39,49)(40,48)(41,54)(43,46)(45,52)(47,53)(51,57)(55,56);(26,28,31,39)(27,32,34,46)(29,37,40,51)(30,43,44,38)(33,45,48,56)(35,49,42,36)(41,55,53,52)(47,57,54,50);(18,20,21,25,22,19,23,24)(26,29,31,40)(27,33,34,48)(28,37,39,51)(30,41,44,53)(32,45,46,56)(35,47,42,54)(36,50,49,57)(38,52,43,55);(27,34)(29,40)(32,46)(35,42)(36,49)(37,51)(41,53)(52,55)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10844);