Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13200 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #127 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1955 |
| prime radical | C17×#525 | C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ G | |
438 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,29,24,28,40,44,25,20,26,32,22,31,39,47)(21,33,37,48,38,30,45,46,35,34,41,49,36,27,42,43);(18,20,23,32,24,31,40,47,25,19,26,29,22,28,39,44)(21,34,41,48,38,27,42,46,35,33,37,49,36,30,45,43);(18,21,22,36,25,35,24,38)(19,27,28,33,20,30,31,34)(23,37,39,42,26,41,40,45)(29,43,44,48,32,46,47,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6188);