Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#23594 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#537 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
1038 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)(20,23)(21,22)(24,25)(26,27)(28,32)(29,39)(30,42)(31,35)(33,41)(34,45)(36,53)(37,51)(38,48)(40,52)(43,47)(44,50)(46,55)(49,56)(54,57);(19,22)(23,25)(26,28,31,38)(27,32,35,48)(29,36,40,54)(30,43,45,37)(33,49,50,46)(34,51,42,47)(39,53,52,57)(41,56,44,55);(26,29,31,40)(27,33,35,50)(28,36,38,54)(30,44,45,41)(32,46,48,49)(34,52,42,39)(37,56,43,55)(47,57,51,53);(18,20,21,24)(19,23,22,25)(29,40)(33,50)(36,54)(39,52)(41,44)(46,49)(53,57)(55,56)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16582);