Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#8997 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | #386 |
| prime radical | C17×#3171 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
452 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22,23,25)(26,27)(28,35,36,39)(29,32,37,38)(30,33)(31,34)(40,41);(20,24)(22,25)(26,28,30,38,31,36,40,32)(27,29,33,39,34,37,41,35);(18,19)(20,25)(21,23)(22,24)(26,29)(27,32)(28,33)(30,39)(31,37)(34,38)(35,40)(36,41)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1985);