Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17405 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#21883 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C17×#117 ◁ G | |
954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
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)(19,22)(20,24)(26,27,31,35,30,34,44,51)(28,36,39,53,38,32,46,48)(29,40,43,52,42,33,45,50)(37,47,54,56,41,49,55,57);(18,19)(20,23)(21,22)(24,25)(26,28)(27,32)(29,41)(30,38)(31,39)(33,49)(34,36)(35,48)(37,42)(40,47)(43,55)(44,46)(45,54)(50,57)(51,53)(52,56);(19,22)(23,25)(26,29,30,42)(27,33,34,40)(28,37,38,41)(31,45,44,43)(32,47,36,49)(35,52,51,50)(39,55,46,54)(48,57,53,56);(18,20,21,24)(19,23,22,25)(27,34)(28,38)(33,40)(35,51)(37,41)(39,46)(50,52)(54,55)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14871);