Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#36725 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
3282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
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)(20,24)(21,25)(22,23)(28,32)(31,33)(35,38)(36,40);(19,23)(20,25)(27,30)(31,33)(34,35,37,38)(36,39,40,41);(26,27)(28,31)(29,30)(32,33)(34,36)(35,39)(37,40)(38,41);(18,20)(19,21)(22,25)(23,24)(26,27)(28,31)(29,30)(32,33)(34,35)(36,39)(37,38)(40,41);(18,21)(19,20)(22,24)(23,25)(26,28)(27,31)(29,32)(30,33)(34,36)(35,39)(37,40)(38,41)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29713);