Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#62011 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#529 ◁ G | |
1856 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 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)(26,27)(28,37)(29,34)(30,36)(31,35)(32,39)(33,38)(40,41);(18,19)(20,23)(21,22)(24,25)(26,28)(27,32)(29,40)(30,39)(31,38)(33,34)(35,41)(36,37);(26,28)(27,33)(29,38)(30,39)(31,40)(32,34)(35,37)(36,41);(19,22)(23,25)(26,29,30,31)(27,34,36,35)(28,38,39,40)(32,41,37,33);(18,20,21,24)(19,23,22,25)(26,29,30,31)(27,35,36,34)(28,38,39,40)(32,33,37,41)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54999);