Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#12988 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #386 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1869 |
| prime radical | C17×#532 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C8×C17 ◁ G | |
466 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)(18,19,23,29,24,27,41,44,25,28,42,46,22,39,31,48)(20,30,34,40,35,45,49,21,33,37,47,36,32,26,43,38);(18,20,31,43,22,32,42,47,25,33,41,49,24,35,23,34)(19,26,44,40,39,37,29,38,28,45,48,36,27,30,46,21);(18,21)(19,20)(22,40)(23,30)(24,36)(25,38)(26,31)(27,35)(28,33)(29,47)(32,39)(34,46)(37,42)(41,45)(43,44)(48,49)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5976);