Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#23674 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C2×#121 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
766 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)(18,19)(20,25)(21,23)(22,24)(26,27,30,35,32,37,31,36)(28,33,39,48,40,49,46,53)(29,41,44,52,45,51,43,34)(38,50,42,56,55,57,54,47);(18,20,22,21)(19,23,24,25)(26,28)(27,33)(29,42)(30,39)(31,46)(32,40)(34,50)(35,48)(36,53)(37,49)(38,43)(41,56)(44,55)(45,54)(47,51)(52,57);(18,21,22,20)(19,23,24,25)(26,29)(27,34)(28,38)(30,43)(31,44)(32,45)(33,47)(35,51)(36,41)(37,52)(39,54)(40,55)(42,46)(48,57)(49,56)(50,53);(26,30,32,31)(27,35,37,36)(28,39,40,46)(29,43,45,44)(33,48,49,53)(34,51,52,41)(38,54,55,42)(47,57,56,50)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16662);