Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18517 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×#120 |
| prime radical | D4×#41×C17 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
1204 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
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)(18,19,21,24)(20,22,25,23)(26,27,31,36)(28,37,40,41)(29,34,30,35)(32,38,33,39);(19,22)(20,25)(23,24)(26,28)(27,32)(29,38)(30,39)(31,40)(33,36)(34,37)(35,41);(26,28)(27,33)(29,38)(30,39)(31,40)(32,36)(34,41)(35,37);(26,29,31,30)(27,34,36,35)(28,38,40,39)(32,37,33,41)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11505);