Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#26751 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C4×C22⋊C4×C17 ◁ G | |
762 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 49 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)(28,31)(29,30)(32,33)(34,35,38,42)(36,43,46,40)(37,47,39,41)(44,49,45,48);(19,22)(23,25)(34,36,38,46)(35,40,42,43)(37,45,39,44)(41,48,47,49);(18,20,21,24)(19,23,22,25)(27,30)(31,33)(36,44)(37,39)(40,48)(41,47)(43,49)(45,46);(19,22)(23,25)(26,28,29,32)(27,31,30,33)(34,37,38,39)(35,41,42,47)(36,45,46,44)(40,48,43,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 19739);