Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24468 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25529 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1014 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)(28,33)(29,40)(30,44)(31,35)(32,36)(34,43)(37,51)(38,49)(39,50)(41,56)(42,53)(45,48)(46,52)(47,55)(54,57);(18,20,21,25)(19,22,23,24)(26,28,32,39)(27,33,36,50)(29,41,42,55)(30,38,31,45)(34,51,52,57)(35,48,44,49)(37,46,54,43)(40,56,53,47);(26,29,30,43,32,42,31,46)(27,34,35,40,36,52,44,53)(28,37,38,55,39,54,45,41)(33,47,48,51,50,56,49,57);(19,23)(22,24)(29,42)(34,52)(37,54)(40,53)(41,55)(43,46)(47,56)(51,57)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18517);