Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18373 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3497 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
1102 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)(20,24)(21,23)(22,25)(26,27,31,35)(28,32,38,45)(29,33,40,47)(30,41,42,34)(36,48,50,43)(37,51,52,44)(39,53,54,46)(49,55,57,56);(19,23)(20,21)(24,25)(26,28)(27,32)(29,36)(30,37)(31,38)(33,43)(34,44)(35,45)(39,49)(40,50)(41,51)(42,52)(46,55)(47,48)(53,56)(54,57);(26,29,31,40)(27,33,35,47)(28,36,38,50)(30,39,42,54)(32,43,45,48)(34,46,41,53)(37,49,52,57)(44,55,51,56);(18,20,22,21)(19,24,25,23)(26,30,31,42)(27,34,35,41)(28,37,38,52)(29,39,40,54)(32,44,45,51)(33,46,47,53)(36,49,50,57)(43,55,48,56)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11361);