Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7453 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#7453 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1365 |
| commutator | C2×C16 | C2×C4×C17 |
| Frattini, cosocle | C4×C16 | C22×C17 |
| prime radical | C22×C17 | #361 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C4×C8×C17 ◁ C4×C16×C17 ◁ G | |
102 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)(18,19,21,28,23,41,20,32,22,40,33,44,34,49,35,27,25,31,39,26,43,30,37,48,24,29,38,47,42,45,36,46);(19,26,31,28)(20,33)(21,35)(22,24)(23,42)(27,30,46,41)(29,47,40,44)(32,45,48,49)(34,43)(36,39)(37,38)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 441);