Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11541 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#13087 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#99 |
| commutator | C24 | C22×C4×C17 |
| Frattini, cosocle | C22×D4 | C23×C17 |
| prime radical | C17×#2404 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C22×#41×C17 ◁ G | |
820 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,25,30,26,29,27,33)(24,28,31,36,32,35,34,37);(22,23,27,30)(24,28,34,36)(25,33,26,29)(31,37,32,35);(19,21)(22,24,26,32)(23,28,29,35)(25,31,27,34)(30,36,33,37)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6075);