Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7457 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#7457 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1368 |
| commutator | C16 | C2×C8×C17 |
| Frattini, cosocle | #346 | C22×C17 |
| prime radical | C22×C17 | #365 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C4×C8×C17 ◁ C17×#346 ◁ G | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 2 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,24,25,34,27,36,39,37)(20,28,29,42)(21,31)(22,33)(26,40,38,35,41,48,47,49)(30,45,44,43)(32,46);(18,19,20,24,21,26,28,35,22,25,30,37,31,38,43,40,23,27,29,36,32,41,42,49,33,39,44,34,46,47,45,48)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 445);