Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#36711 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| prime radical | C23×D4×C17 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2422 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)(30,31,36,39)(32,34,33,37)(35,43,44,38)(40,45,41,42);(23,26)(27,29)(30,32,36,33)(31,37,39,34)(35,40,44,41)(38,45,43,42);(18,19)(20,21)(22,23)(24,27)(25,26)(28,29)(30,33,36,32)(31,37,39,34)(35,41,44,40)(38,45,43,42);(22,23)(24,27)(25,26)(28,29)(30,34,36,37)(31,32,39,33)(35,42,44,45)(38,40,43,41);(22,24)(23,27)(25,28)(26,29)(30,35)(31,38)(32,40)(33,41)(34,42)(36,44)(37,45)(39,43)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29699);