Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17386 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#538 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×D4×C17 ◁ G | |
1080 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)(18,19,21,26,23,27,32,40)(20,25,30,38,28,39,42,49)(22,24,31,35,33,36,45,47)(29,34,43,46,41,37,44,48);(19,24)(20,28)(21,31)(25,37)(27,36)(29,41)(30,44)(32,45)(34,39)(38,49)(42,43)(46,48);(18,20)(19,25)(21,30)(22,29)(23,28)(24,34)(26,38)(27,39)(31,43)(32,42)(33,41)(35,46)(36,37)(40,49)(44,45)(47,48);(20,29)(25,34)(28,41)(30,43)(37,39)(38,46)(42,44)(48,49)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10374);