Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#7175 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #102 |
| commutator | C8 | C4×C8×C17 |
| Frattini, cosocle | C2×C4×C8 | C22×C17 |
| socle | C22×C17 | #340 |
| prime radical | C23×C17 | #102 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 2 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,24,22,25,20,23)(26,27,30,34)(28,29,36,38)(31,33,39,41)(32,40,37,35);(19,23,25,24)(26,28,31,35,32,33,38,34,30,36,39,40,37,41,29,27)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 163);