Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#26749 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C4×C22⋊C4×C17 ◁ G | |
720 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)(34,35,39,43)(36,40,46,49)(37,41,38,42)(44,47,45,48);(19,22)(23,25)(34,36,39,46)(35,40,43,49)(37,45,38,44)(41,48,42,47);(18,20,21,24)(19,23,22,25)(27,30)(31,33)(36,44)(37,38)(40,47)(41,42)(45,46)(48,49);(19,22)(23,25)(26,28,29,32)(27,31,30,33)(34,37,39,38)(35,41,43,42)(36,45,46,44)(40,48,49,47)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 19737);