Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#23833 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C2×C17 | #2398 |
| prime radical | C17×#575 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ G | |
616 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(20,29,32,42)(21,26)(22,27)(23,37)(24,28)(25,33,39,30)(31,43,45,49)(34,40)(35,47)(36,41)(38,46,48,44);(20,30,32,33)(25,29,39,42)(31,44,45,46)(38,43,48,49);(18,20)(19,25)(21,31)(22,30)(23,33)(24,32)(26,38)(27,42)(28,39)(29,37)(34,44)(35,46)(36,45)(40,49)(41,48)(43,47);(18,21,22,34,24,36,23,35)(19,26,27,40,28,41,37,47)(20,31,30,44,32,45,33,46)(25,38,42,49,39,48,29,43)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16821);