Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18417 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3535 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
928 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,24)(22,25)(26,32)(27,30)(28,31)(29,33)(34,35,38,40)(36,42,44,49)(37,45,47,41)(39,46,48,43);(18,20)(19,23)(21,26)(22,27)(24,29)(25,30)(28,33)(31,32)(34,36,38,44)(35,39,40,48)(37,46,47,43)(41,49,45,42);(18,21)(19,24)(20,26)(22,28)(23,29)(25,31)(27,33)(30,32)(34,35)(36,39)(37,45)(38,40)(41,47)(42,46)(43,49)(44,48);(19,25)(23,30)(24,31)(29,32)(35,40)(39,48)(41,45)(42,49)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11405);