Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#36708 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| prime radical | C25×C17 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(24,28)(27,29)(30,31,35,38)(32,33,40,36)(34,42,43,37)(39,44,45,41);(23,26)(27,29)(30,32,35,40)(31,36,38,33)(34,39,43,45)(37,44,42,41);(18,19)(20,21)(22,23)(24,27)(25,26)(28,29);(22,23)(24,27)(25,26)(28,29)(30,33,35,36)(31,32,38,40)(34,41,43,44)(37,39,42,45);(22,24)(23,27)(25,28)(26,29)(30,34)(31,37)(32,39)(33,41)(35,43)(36,44)(38,42)(40,45)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29696);