Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C23×C42 |
| direct product | C17×#10948 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C23×D4×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1074 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)(22,23)(24,30,33,28)(25,34)(26,35)(27,29)(31,32,37,36);(18,19,20,21)(22,24)(23,28)(25,31)(26,36)(27,33)(29,30)(32,34)(35,37);(22,25,34,23,27,35,26,29)(24,31,32,28,33,37,36,30)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3936);