Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17447 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C17 | C2×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C22×C22⋊C4 |
| prime radical | C22×#41×C17 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C17 ◁ C22×C42×C17 ◁ G | |
1332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,23,21,22,24,25)(26,27,30,33,31,28,29,32);(26,28)(27,31)(29,33)(30,32);(19,22)(23,25);(26,29,31,30)(27,32,28,33)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10435);