Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C17 · Schur multiplier (H2) = C213 |
| direct product | C17×#62686 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C17 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C17 |
| socle | C22×C17 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C17 ◁ G | |
7226 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 6 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27)(28,31)(29,33)(30,32)(34,37)(35,38)(36,39)(40,41);(19,22)(23,25)(26,28)(27,31)(29,35)(30,34)(32,37)(33,38)(36,40)(39,41);(27,32)(28,34)(33,39)(35,40);(27,32)(31,37)(33,39)(38,41);(26,29,30,36)(27,33,32,39)(28,35,34,40)(31,38,37,41);(18,20,21,24)(19,23,22,25)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55674);