Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#17868 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C17 | C2×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C2×C17×#135 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
688 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20,22,23,25,24)(26,27)(28,35)(29,34)(30,38)(31,33)(32,36)(37,41)(39,40);(26,28)(27,32)(29,36)(30,39)(31,37)(33,40)(34,41)(35,38);(18,20,21,23,22,24,25,19)(27,33)(32,40)(34,38)(35,41);(26,29,31,30)(27,34,33,38)(28,36,37,39)(32,41,40,35)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10856);