Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#34208 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C2×C17×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
3054 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
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)(19,21)(22,23,25,24)(26,27)(28,34)(29,37)(30,31)(32,36)(33,38)(35,39)(40,41);(22,24,25,23)(27,31)(32,34)(33,37)(39,40);(18,19,20,21)(26,28)(27,32)(29,35)(30,36)(31,34)(33,39)(37,40)(38,41);(26,27)(28,32)(29,33)(30,31)(34,36)(35,39)(37,38)(40,41);(26,29,30,38)(27,33,31,37)(28,35,36,41)(32,39,34,40)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27196);