Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #7092 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#7093 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C17 | #331 |
| commutator | C4×C8 | C2×C4×C17 |
| Frattini, cosocle | C82 | C22×C17 |
| LCS | G ▷ C4×C8 ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ C82×C17 ◁ G | |
130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 4352 |
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)(19,24,25,32)(20,28)(21,22)(26,29,27,33)(30,31)(34,35,37,41,47,46,49,44,38,42,48,40,39,36,43,45);(18,19,23,25)(20,29,31,33)(21,27,22,26)(24,28,32,30)(34,36)(35,39)(37,41)(38,46)(40,48)(42,47)(43,44)(45,49)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 81);