Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of #7529 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C4 |
| direct product | C17×#7531 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1408 |
| commutator | C4×C8 | C2×C4×C17 |
| Frattini, cosocle | #494 | C22×C17 |
| prime radical | C17×#493 | C4 |
| LCS | G ▷ C4×C8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C17 ◁ C2×C4×C17 ◁ C42×C17 ◁ C17×#494 ◁ G | |
146 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)(18,19,21,27,24,29,37,44)(20,26,31,42,33,40,47,49)(22,28,36,45,23,38,35,43)(25,34,39,32,41,46,48,30);(19,25)(20,30)(22,23)(26,28)(27,42)(29,41)(31,34)(32,33)(35,36)(38,40)(39,43)(44,49)(45,48)(46,47)425 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 519);