Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1426 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#7464 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #367 |
| commutator | C16 | C2×C8×C17 |
| Frattini, cosocle | C4×C16 | C22×C17 |
| socle | C2×C17 | #1372 |
| prime radical | C22×C17 | #368 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C2×C8×C17 ◁ C4×C8×C17 ◁ C4×C16×C17 ◁ G | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 2 generators on 81 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,28,24,29,45,55,25,31,40,59,47,30,23,46)(20,32,35,61,37,63,36,73,38,65,44,62,74,64,75,81)(21,39,33,56,42,76,66,58,43,77,67,57,72,49,41,27)(26,48,50,79,52,80,78,34,54,68,51,70,53,69,60,71);(18,20,33,48,23,36,21,34,47,74,41,69,40,35,72,79,25,38,67,68,45,75,43,71,24,37,66,80,22,44,42,70)(19,26,49,73,28,51,27,32,29,52,39,62,55,60,56,63,31,54,76,81,59,50,58,65,30,53,77,61,46,78,57,64)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 452);