Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#33690 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#2190 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C4×M16×C17 ◁ G | |
526 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)(20,25)(21,31)(22,35)(23,39)(24,28)(26,34)(27,36)(29,46)(30,45)(32,44)(33,48)(37,40)(38,43)(41,47)(42,49);(18,20,24,23)(19,25,28,39)(21,29,33,32)(22,36,38,30)(26,40,41,42)(27,43,45,35)(31,44,48,46)(34,49,47,37);(18,21)(19,26)(20,29)(22,37)(23,32)(24,33)(25,40)(27,44)(28,41)(30,47)(31,35)(34,36)(38,49)(39,42)(43,48)(45,46);(21,32,33,29)(22,38)(26,40,41,42)(27,45)(30,36)(31,44,48,46)(34,37,47,49)(35,43)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26678);