Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#34381 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C25×C17 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2134 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)(18,19,20,21)(23,26)(24,28)(30,31)(32,35)(33,38)(34,39)(36,40)(37,42)(41,43)(44,45);(23,26)(27,29)(31,32)(33,40)(37,39)(41,45);(22,23)(24,27)(25,26)(28,29)(30,32,35,31)(33,38,40,36)(34,39,42,37)(41,44,45,43);(22,24,25,28)(23,27,26,29)(30,33)(31,36)(32,38)(34,41)(35,40)(37,43)(39,44)(42,45);(30,34)(31,37)(32,39)(33,41)(35,42)(36,43)(38,44)(40,45)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27369);