Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61413 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3155 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#533 ◁ G | |
1886 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23)(24,25)(26,27,31,36)(28,37,39,33)(29,41,43,50)(30,35,32,45)(34,46,51,42)(38,53,54,57)(40,49,44,48)(47,56,52,55);(18,19,22,23)(20,24,21,25)(26,28,31,39)(27,33,36,37)(29,38,43,54)(30,44,32,40)(34,47,51,52)(35,49,45,48)(41,57,50,53)(42,56,46,55);(18,20,22,21)(19,24,23,25)(26,29,31,43)(27,34,36,51)(28,38,39,54)(30,42,32,46)(33,47,37,52)(35,50,45,41)(40,55,44,56)(48,57,49,53);(18,21,22,20)(19,24,23,25)(28,39)(33,37)(38,54)(40,44)(47,52)(48,49)(53,57)(55,56);(26,30,31,32)(27,35,36,45)(28,40,39,44)(29,42,43,46)(33,48,37,49)(34,50,51,41)(38,55,54,56)(47,57,52,53)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54401);