Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18192 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18200 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3490 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1078 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)(18,19,23,27)(20,28,31,44)(21,32,34,46)(22,25,36,40)(24,37,38,30)(26,41,43,35)(29,42,45,49)(33,39,47,48);(18,20)(19,24)(21,33)(22,29)(23,31)(25,39)(26,42)(27,38)(28,32)(30,35)(34,47)(36,45)(37,41)(40,48)(43,49)(44,46);(21,34)(26,43)(28,44)(30,37)(32,46)(33,47)(35,41)(42,49);(19,25)(20,29)(26,32)(27,40)(30,33)(31,45)(37,47)(43,46)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11188);