Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18522 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×#120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
1000 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)(19,23)(20,21)(24,25)(26,27)(28,37)(29,40)(30,34)(31,35)(32,36)(33,39)(38,41);(18,19,22,24)(20,23,21,25)(26,28,32,29)(27,33,36,41)(30,38,31,39)(34,37,35,40);(18,20,22,21)(19,23,24,25)(26,29,32,28)(27,33,36,41)(30,39,31,38)(34,37,35,40);(26,30,32,31)(27,34,36,35)(28,38,29,39)(33,37,41,40)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11510);