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×#33689 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#575 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C4×M16×C17 ◁ G | |
520 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)(20,28,30,46)(21,33,34,49)(22,38,36,26)(24,39,41,31)(25,43,44,37)(29,45,32,48)(35,40,47,42);(21,34)(25,44)(28,46)(31,39)(33,49)(35,47)(37,43)(45,48);(18,20)(19,24)(21,35)(22,29)(23,30)(25,45)(26,40)(27,41)(28,33)(31,37)(32,36)(34,47)(38,42)(39,43)(44,48)(46,49);(20,29,30,32)(21,34)(24,40,41,42)(25,44)(28,45,46,48)(31,35,39,47)(33,49)(37,43)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26677);