Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12506 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C8 |
| direct product | C17×#12514 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C17 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C17 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ C82×C17 ◁ G | |
246 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 3 generators on 65 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26)(21,29)(22,24)(23,27)(25,30)(28,32)(31,33)(34,35,42,49)(36,50,55,44)(37,56,51,43)(38,46,57,65)(39,45,59,63)(40,48,41,47)(52,62,58,61)(53,64,54,60);(18,20,21,27,22,28,30,33)(19,23,25,26,24,31,29,32)(34,36,39,52,40,53,57,37,42,55,59,58,41,54,38,51)(35,43,46,60,47,61,63,44,49,56,65,64,48,62,45,50);(19,24)(23,31)(25,29)(26,32)(34,37,57,54,41,52,39,55,42,51,38,53,40,58,59,36)(35,44,63,62,48,60,46,56,49,50,45,61,47,64,65,43)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5502);