Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#7932 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C17 | C22⋊C4 |
| commutator | C22 | C2×C4×C8×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | C2×#95 |
| prime radical | C24×C17 | C42 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C17 ◁ C22×C42×C17 ◁ G | |
666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,24,23,25,22,20)(26,27)(28,36,38,32)(29,33)(30,35)(31,34)(37,41,39,40);(18,20,22,25,23,24,21,19)(26,28,30,39,31,38,29,37)(27,32,35,41,34,36,33,40);(26,29,31,30)(27,33,34,35)(28,37,38,39)(32,40,36,41)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 920);