Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18518 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×#120 |
| prime radical | C17×#3035 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
968 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(20,24)(23,25)(26,27)(28,34)(29,33)(30,35)(31,36)(32,37)(38,41)(39,40);(18,19,21,23)(20,25,24,22)(26,28,32,39)(27,33,37,41)(29,30,38,31)(34,36,40,35);(26,29)(27,34)(28,30)(31,39)(32,38)(33,36)(35,41)(37,40);(26,30,32,31)(27,35,37,36)(28,38,39,29)(33,34,41,40)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11506);