Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#34371 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C24×C17 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2238 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 2176 |
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)(18,19,20,21)(22,23,26,24)(25,28,29,27)(31,36)(32,33)(34,42)(44,45);(23,24)(27,28)(30,31,35,36)(32,38,33,37)(34,39,42,43)(40,45,41,44);(30,32,35,33)(31,37,36,38)(34,40,42,41)(39,44,43,45);(22,24,26,23)(25,28,29,27)(30,33,35,32)(31,38,36,37)(34,41,42,40)(39,45,43,44);(22,25)(23,27)(24,28)(26,29)(30,34)(31,39)(32,40)(33,41)(35,42)(36,43)(37,44)(38,45)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27359);