Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#62151 |
| 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 ◁ C4×#41×C17 ◁ G | |
1986 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)(18,19,20,22)(21,23,25,24)(26,27,30,33)(28,34,35,31)(29,37,38,32)(36,39,41,40);(19,22)(23,24)(26,28)(27,31)(29,36)(30,35)(32,39)(33,34)(37,40)(38,41);(19,23)(21,25)(22,24);(19,22)(23,24)(28,35)(31,34)(36,41)(39,40);(19,22)(23,24)(26,29,30,38)(27,32,33,37)(28,36,35,41)(31,39,34,40)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55139);