Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#23525 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #394 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C2×C17 | C2×#394 |
| prime radical | C2×C17×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
1332 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)(20,30)(21,35)(22,27)(23,28)(24,29)(25,33)(26,38)(31,42)(32,41)(34,45)(36,40)(37,44)(39,43)(46,48)(47,49);(18,20)(19,25)(21,36)(22,32)(23,33)(24,34)(26,42)(27,30)(28,45)(29,41)(31,39)(35,49)(37,48)(38,47)(40,44)(43,46);(18,21,22,37,24,39,23,38)(19,26,28,43,29,44,27,35)(20,31,33,48,34,36,32,47)(25,40,30,46,41,42,45,49);(18,22,24,23)(19,27,29,28)(20,32,34,33)(21,37,39,38)(25,30,41,45)(26,35,44,43)(31,47,36,48)(40,46,42,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16513);