Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18243 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3561 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×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)(23,29)(30,33)(34,35,39,42)(36,43,45,48)(37,41,38,46)(40,47,49,44);(18,19)(20,23)(21,24)(22,25)(26,30)(27,29)(28,31)(32,33)(34,36,39,45)(35,40,42,49)(37,44,38,47)(41,48,46,43);(18,20)(19,23)(21,26)(22,27)(24,30)(25,29)(28,32)(31,33)(37,38)(41,46)(43,48)(44,47);(18,21,22,28)(19,24,25,31)(20,26,27,32)(23,30,29,33)(34,37,39,38)(35,41,42,46)(36,44,45,47)(40,48,49,43)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11231);