Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18385 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3505 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1012 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(18,19,24,21)(20,30,35,45)(22,28,23,37)(25,29,41,38)(26,32,31,33)(27,39,36,40)(34,44,49,42)(43,48,47,46);(18,20)(19,26)(21,31)(22,33)(23,32)(24,35)(25,34)(27,44)(28,45)(29,43)(30,37)(36,42)(38,47)(39,46)(40,48)(41,49);(18,21,24,19)(20,31,35,26)(22,36,23,27)(25,38,41,29)(28,40,37,39)(30,46,45,48)(32,44,33,42)(34,47,49,43);(18,22,24,23)(19,27,21,36)(20,32,35,33)(25,39,41,40)(26,42,31,44)(28,29,37,38)(30,43,45,47)(34,48,49,46)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11373);