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×#7532 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1408 |
| commutator | C4×C8 | C2×C4×C17 |
| Frattini, cosocle | #494 | C22×C17 |
| prime radical | C22×C17 | #353 |
| LCS | G ▷ C4×C8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C17 ◁ C2×C4×C17 ◁ C42×C17 ◁ C17×#494 ◁ G | |
136 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)(18,19,22,28,25,30,20,31)(21,27,36,43,39,46,35,26)(23,29,33,44,24,41,34,47)(32,48,37,45,40,42,38,49);(18,20,25,22)(19,26,30,43)(21,35,39,36)(23,34,24,33)(27,44,46,47)(28,45,31,49)(29,48,41,42)(32,38,40,37)425 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 520);